Publications

Submissions

Gary Froyland.
A tutorial on the dynamic Laplacian. Submitted. Submitted version

Jason Atnip, Gary Froyland, and Péter Koltai.
An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Anthony Quas.
Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products. Submitted. Submitted version

Gary Froyland and Stefano Galatolo.
Optimal linear response for expanding circle maps. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Compound Poisson statistics for dynamical systems via spectral perturbation. Submitted. arXiv version

Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, and Péter Koltai.
A dynamic p-Laplacian. Submitted. arXiv version

Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: A tutorial on the dynamic Laplacian. Submitted. Submitted version
Jason Atnip, Gary Froyland, and Péter Koltai.
An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Anthony Quas.
Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products. Submitted. Submitted version

Gary Froyland and Stefano Galatolo.
Optimal linear response for expanding circle maps. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Compound Poisson statistics for dynamical systems via spectral perturbation. Submitted. arXiv version

Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, and Péter Koltai.
A dynamic p-Laplacian. Submitted. arXiv version

Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets. Submitted. arXiv version
Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Anthony Quas.
Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products. Submitted. Submitted version

Gary Froyland and Stefano Galatolo.
Optimal linear response for expanding circle maps. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Compound Poisson statistics for dynamical systems via spectral perturbation. Submitted. arXiv version

Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, and Péter Koltai.
A dynamic p-Laplacian. Submitted. arXiv version

Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products. Submitted. Submitted version
Gary Froyland and Stefano Galatolo.
Optimal linear response for expanding circle maps. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Compound Poisson statistics for dynamical systems via spectral perturbation. Submitted. arXiv version

Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, and Péter Koltai.
A dynamic p-Laplacian. Submitted. arXiv version

Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: Optimal linear response for expanding circle maps. Submitted. arXiv version
Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Compound Poisson statistics for dynamical systems via spectral perturbation. Submitted. arXiv version

Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, and Péter Koltai.
A dynamic p-Laplacian. Submitted. arXiv version

Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: Compound Poisson statistics for dynamical systems via spectral perturbation. Submitted. arXiv version
Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, and Péter Koltai.
A dynamic p-Laplacian. Submitted. arXiv version

Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: A dynamic p-Laplacian. Submitted. arXiv version
Gary Froyland and Christopher P. Rock.
Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version

Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions Submitted. arXiv version
Michael Denes, Shane R. Keating, and Gary Froyland.
Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version: Bathymetry imposes a global pattern of cross-front transport in the Southern Ocean. Submitted. arXiv version
Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version: Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems. Submitted. arXiv version

Edited books

Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle.

Advances in Dynamics, Optimization and Computation: A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Studies in Systems, Decision and Control, volume 304, Springer, 2020. Springer website

Wael Bahsoun, Chris Bose, and Gary Froyland.

Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, volume 70, Springer, 2014. Springer website: Advances in Dynamics, Optimization and Computation: A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Studies in Systems, Decision and Control, volume 304, Springer, 2020. Springer website
Wael Bahsoun, Chris Bose, and Gary Froyland.

Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, volume 70, Springer, 2014. Springer website: Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, volume 70, Springer, 2014. Springer website

Refereed Book Chapters

Anna Klünker, Christiane Schneide, Gary Froyland, Jörg Schumacher, and Kathrin Padberg-Gehle.

Set-oriented and finite-element study of coherent behavior in Rayleigh-Bénard convection. In Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, editors, Advances in Dynamics, Optimization and Computation. Studies in Systems, Decision and Control, volume 304, pages 86-108, Springer, 2020. Published version

Gary Froyland and Kathrin Padberg-Gehle.

Almost-invariant and finite-time coherent sets: directionality, duration, and diffusion. In Wael Bahsoun, Chris Bose, Gary Froyland, editors, Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, volume 70, pages 171-216, Springer, 2014. Accepted version.

Gary Froyland.
Extracting dynamical behaviour via Markov models. In Alistair Mees, editor, Nonlinear Dynamics and Statistics: Proceedings, Newton Institute, Cambridge, 1998, pages 283-324, Birkhauser, 2001. Contents | pdf file | MathReviews doc

Michael Dellnitz, Gary Froyland, and Oliver Junge.
The algorithms behind GAIO -- Set oriented numerical methods for dynamical systems. In Bernold Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 145-174, Springer 2001. Abstract | final version | MathReviews doc: Set-oriented and finite-element study of coherent behavior in Rayleigh-Bénard convection. In Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, editors, Advances in Dynamics, Optimization and Computation. Studies in Systems, Decision and Control, volume 304, pages 86-108, Springer, 2020. Published version
Gary Froyland and Kathrin Padberg-Gehle.

Almost-invariant and finite-time coherent sets: directionality, duration, and diffusion. In Wael Bahsoun, Chris Bose, Gary Froyland, editors, Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, volume 70, pages 171-216, Springer, 2014. Accepted version.

Gary Froyland.
Extracting dynamical behaviour via Markov models. In Alistair Mees, editor, Nonlinear Dynamics and Statistics: Proceedings, Newton Institute, Cambridge, 1998, pages 283-324, Birkhauser, 2001. Contents | pdf file | MathReviews doc

Michael Dellnitz, Gary Froyland, and Oliver Junge.
The algorithms behind GAIO -- Set oriented numerical methods for dynamical systems. In Bernold Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 145-174, Springer 2001. Abstract | final version | MathReviews doc: Almost-invariant and finite-time coherent sets: directionality, duration, and diffusion. In Wael Bahsoun, Chris Bose, Gary Froyland, editors, Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, volume 70, pages 171-216, Springer, 2014. Accepted version.
Gary Froyland.
Extracting dynamical behaviour via Markov models. In Alistair Mees, editor, Nonlinear Dynamics and Statistics: Proceedings, Newton Institute, Cambridge, 1998, pages 283-324, Birkhauser, 2001. Contents | pdf file | MathReviews doc

Michael Dellnitz, Gary Froyland, and Oliver Junge.
The algorithms behind GAIO -- Set oriented numerical methods for dynamical systems. In Bernold Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 145-174, Springer 2001. Abstract | final version | MathReviews doc: Extracting dynamical behaviour via Markov models. In Alistair Mees, editor, Nonlinear Dynamics and Statistics: Proceedings, Newton Institute, Cambridge, 1998, pages 283-324, Birkhauser, 2001. Contents | pdf file | MathReviews doc
Michael Dellnitz, Gary Froyland, and Oliver Junge.
The algorithms behind GAIO -- Set oriented numerical methods for dynamical systems. In Bernold Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 145-174, Springer 2001. Abstract | final version | MathReviews doc: The algorithms behind GAIO -- Set oriented numerical methods for dynamical systems. In Bernold Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 145-174, Springer 2001. Abstract | final version | MathReviews doc

Refereed Journal Articles

Gary Froyland, Dimitrios Giannakis, Edoardo Luna, and Joanna Slawinska.
Revealing trends and persistent cycles of non-autonomous systems with autonomous operator-theoretic techniques. Nature Communications, 15:4268-, 2024. Journal article

Gary Froyland and Péter Koltai.
Detecting the birth and death of finite-time coherent sets. To appear in Communications on Pure and Applied Mathematics, 76:3642–3684, 2023. Journal article

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Equilibrium states for non-transitive random open and closed dynamical systems. Ergodic Theory and Dynamical Systems, 43(10):3193-3215, 2023. arXiv version

Fadi Antown, Gary Froyland, and Stefano Galatolo.
Optimal linear response for Markov Hilbert-Schmidt integral operators and stochastic dynamical systems. Journal of Nonlinear Science, 32(article number 79):1-60, 2022. Journal article

Michael C. Denes, Gary Froyland, and Shane R. Keating.
Persistence and material coherence of an ocean eddy. Physical Review Fluids, 7(3):034501, 2022. Journal article

Wolf-Juergen Beyn, Gary Froyland, and Thorsten Huels.
Angular values of nonautonomous and random linear dynamical systems. SIAM Journal on Applied Dynamical Systems, 21(2):1245-1286, 2022. Submitted version

Ryan Abernathey, Christopher Bladwell, Gary Froyland, and Konstantinos Sakellariou.
Deep Lagrangian connectivity in the global ocean inferred from Argo floats. Journal of Physical Oceanography, 52(5):951-963, 2022. Journal article

Gary Froyland, Dimitrios Giannakis, Benjamin Lintner, Maxwell Pike, and Joanna Slawinska.
Spectral analysis of climate dynamics with operator-theoretic approaches. Nature Communications, 12:6570- , 2021. Journal article

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article

Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Revealing trends and persistent cycles of non-autonomous systems with autonomous operator-theoretic techniques. Nature Communications, 15:4268-, 2024. Journal article
Gary Froyland and Péter Koltai.
Detecting the birth and death of finite-time coherent sets. To appear in Communications on Pure and Applied Mathematics, 76:3642–3684, 2023. Journal article: Detecting the birth and death of finite-time coherent sets. To appear in Communications on Pure and Applied Mathematics, 76:3642–3684, 2023. Journal article
Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Equilibrium states for non-transitive random open and closed dynamical systems. Ergodic Theory and Dynamical Systems, 43(10):3193-3215, 2023. arXiv version: Equilibrium states for non-transitive random open and closed dynamical systems. Ergodic Theory and Dynamical Systems, 43(10):3193-3215, 2023. arXiv version
Fadi Antown, Gary Froyland, and Stefano Galatolo.
Optimal linear response for Markov Hilbert-Schmidt integral operators and stochastic dynamical systems. Journal of Nonlinear Science, 32(article number 79):1-60, 2022. Journal article

Michael C. Denes, Gary Froyland, and Shane R. Keating.
Persistence and material coherence of an ocean eddy. Physical Review Fluids, 7(3):034501, 2022. Journal article

Wolf-Juergen Beyn, Gary Froyland, and Thorsten Huels.
Angular values of nonautonomous and random linear dynamical systems. SIAM Journal on Applied Dynamical Systems, 21(2):1245-1286, 2022. Submitted version

Ryan Abernathey, Christopher Bladwell, Gary Froyland, and Konstantinos Sakellariou.
Deep Lagrangian connectivity in the global ocean inferred from Argo floats. Journal of Physical Oceanography, 52(5):951-963, 2022. Journal article

Gary Froyland, Dimitrios Giannakis, Benjamin Lintner, Maxwell Pike, and Joanna Slawinska.
Spectral analysis of climate dynamics with operator-theoretic approaches. Nature Communications, 12:6570- , 2021. Journal article

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article

Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimal linear response for Markov Hilbert-Schmidt integral operators and stochastic dynamical systems. Journal of Nonlinear Science, 32(article number 79):1-60, 2022. Journal article
Michael C. Denes, Gary Froyland, and Shane R. Keating.
Persistence and material coherence of an ocean eddy. Physical Review Fluids, 7(3):034501, 2022. Journal article: Persistence and material coherence of an ocean eddy. Physical Review Fluids, 7(3):034501, 2022. Journal article
Wolf-Juergen Beyn, Gary Froyland, and Thorsten Huels.
Angular values of nonautonomous and random linear dynamical systems. SIAM Journal on Applied Dynamical Systems, 21(2):1245-1286, 2022. Submitted version

Ryan Abernathey, Christopher Bladwell, Gary Froyland, and Konstantinos Sakellariou.
Deep Lagrangian connectivity in the global ocean inferred from Argo floats. Journal of Physical Oceanography, 52(5):951-963, 2022. Journal article

Gary Froyland, Dimitrios Giannakis, Benjamin Lintner, Maxwell Pike, and Joanna Slawinska.
Spectral analysis of climate dynamics with operator-theoretic approaches. Nature Communications, 12:6570- , 2021. Journal article

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article

Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Angular values of nonautonomous and random linear dynamical systems. SIAM Journal on Applied Dynamical Systems, 21(2):1245-1286, 2022. Submitted version
Ryan Abernathey, Christopher Bladwell, Gary Froyland, and Konstantinos Sakellariou.
Deep Lagrangian connectivity in the global ocean inferred from Argo floats. Journal of Physical Oceanography, 52(5):951-963, 2022. Journal article

Gary Froyland, Dimitrios Giannakis, Benjamin Lintner, Maxwell Pike, and Joanna Slawinska.
Spectral analysis of climate dynamics with operator-theoretic approaches. Nature Communications, 12:6570- , 2021. Journal article

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article

Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Deep Lagrangian connectivity in the global ocean inferred from Argo floats. Journal of Physical Oceanography, 52(5):951-963, 2022. Journal article
Gary Froyland, Dimitrios Giannakis, Benjamin Lintner, Maxwell Pike, and Joanna Slawinska.
Spectral analysis of climate dynamics with operator-theoretic approaches. Nature Communications, 12:6570- , 2021. Journal article

Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article

Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Spectral analysis of climate dynamics with operator-theoretic approaches. Nature Communications, 12:6570- , 2021. Journal article
Jason Atnip, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.
Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article

Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386:819–902, 2021. Journal article
Fadi Antown, Gary Froyland, and Oliver Junge.
Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article

Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Linear response for the dynamic Laplacian and finite-time coherent sets. Nonlinearity, 34:3337- , 2021. Journal article
Harry Crimmins and Gary Froyland.
Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article

Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Fourier approximation of the statistical properties of Anosov maps on tori. Nonlinearity, 33(11):6244- , 2020. Journal article
Gary Froyland, Péter Koltai, and Martin Stahn.
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article

Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. SIAM Journal on Applied Dynamical Systems, 19(3):1659–1700, 2020. Journal article
Nathanael Schilling, Gary Froyland, and Oliver Junge.
Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version

Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Higher-Order Finite Element Approximation of the Dynamic Laplacian. ESAIM: Mathematical Modelling and Numerical Analysis, 54:1777–1795, 2020. Revised version
Michelle Dunbar, Ricky O'Brian, and Gary Froyland.

Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimal lung imaging for cancer radiation therapy. European Journal of Operational Research, 282(3):1038-1052, 2020. Journal article
Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article

Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373:629-664, 2020. Journal article
Harry Crimmins and Gary Froyland.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article

Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps. Annales Henri Poincaré, 20:3113–3161, 2019. Journal article
Gary Froyland, Christopher P. Rock, and Konstantinos Sakellariou.

Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification.Communications in Nonlinear Science and Numerical Simulation, 77:81-107, 2019. Journal article
Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Gary Froyland, Julio Sheinbaum, and Paula Perez-Brunius.

Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Lagrangian geography of the deep Gulf of Mexico. Journal of Physical Oceanography, 49:269-290, 2019. Journal article
Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39(10):2769-2792, 2019. Journal article
Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article

Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372:2357-2388, 2019. Journal article
Gary Froyland and Oliver Junge.

Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories.SIAM Journal on Applied Dynamical Systems, 17(2):1891-1924, 2018. Journal article
Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version

Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360(3):1121-1187, 2018. Firstview version
Fadi Antown, Davor Dragičević, and Gary Froyland.

Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article

Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimal linear responses for Markov chains and stochastically perturbed dynamical systems. Journal of Statistical Physics, 170:1051-1087, 2018. Journal article
Davor Dragičević, Gary Froyland, Cecilia González-Tokman, and Sandro Vaienti.

Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article

Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31:2252-2280, 2018. Journal article
Davor Dragičević and Gary Froyland.

Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version

Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Hölder continuity of Oseledets splittings for semi-invertible operator cocycles. Ergodic Theory and Dynamical Systems, 38:3, 961–981, 2018. Firstview version
Gary Froyland and Naratip Santitissadeekorn.

Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version

Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimal mixing enhancement. SIAM Journal on Applied Mathematics, 77(4):1444-1470, 2017. Arxiv version | High resolution version
Philippe Miron, Francesco J. Beron-Vera, Maria J. Olascoaga, Julio Sheinbaum, Paula Perez-Brunius, and Gary Froyland.

Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article

Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Lagrangian dynamical geography of the Gulf of Mexico. Scientific Reports - Nature, 7:7021, 2017. Journal article
Gary Froyland and Eric Kwok.

A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version

Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds.Journal of Nonlinear Science, 30:1889–1971, 2020 (published online June 2017). Proof version
Alireza Hadjighasem, Mohammad Farazmand, Daniel Blazevski, Gary Froyland, and George Haller.

A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article

Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A Critical Comparison of Lagrangian Methods for Coherent Structure Detection. Chaos, 27:053104, 2017. Journal article
Gary Froyland and Péter Koltai.

Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Estimating long-term behavior of periodically driven flows without trajectory integration. Nonlinearity, 30:1948-1986, 2017. Journal article
Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A trajectory-free framework for analysing multiscale systems. Physica D, 328-329:pp34-43, 2016. Journal article
Natashia Boland, Irina Dumitrescu, Gary Froyland, and Thomas Kalinowski.

Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article

Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Minimum Cardinality Non-Anticipativity Constraint Sets for Multistage Stochastic Programming with Endogeneous Observation of Uncertainty. Mathematical Programming, Series B, 157(1):69-93, 2016. Journal article
Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson.

Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article

Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimal mixing enhancement by local perturbation. SIAM Review, 58(3):494-513, 2016. Journal article
Gary Froyland and Robyn M. Stuart.

Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article

Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Cheeger inequalities for absorbing Markov chains. Advances in Applied Probability, 48(3), 2016. Journal article
Gary Froyland and Cecilia González-Tokman.

Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version

Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Stability and approximation of random invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16(1):1650003, 2016. Submitted version
Gary Froyland and Oliver Junge.

On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version

Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: On fast computation of finite-time coherent sets using radial basis functions. Chaos, 25:087409, 2015. Submitted version
Gary Froyland and Kathrin Padberg-Gehle.

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version

Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos, 25:087406, 2015. Submitted version
Thomas Peacock, Gary Froyland, and George Haller.

Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article

Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Introduction to Focus Issue: Objective Detection of Coherent Structures. Chaos, 25:087201, 2015. Link to Journal Article
Gary Froyland.

Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015. Journal article
Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version

Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Stochastic stability of Lyapunov exponents and Oseledets splitting for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68(11):2052-2081, 2015. Accepted version
Gary Froyland, Christian Horenkamp, Vincent Rossi, and Erik van Sebille.

Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article

Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets. Chaos, 25:083119, 2015. Journal article
Gary Froyland and Eric Kwok.

Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version

David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Partitions of networks that are robust to vertex permutation dynamics. Special Matrices, 3:22-42, 2015. Proof version
David M. Walker, Antoinette Tordesillas, Nicolas Brodu, Joshua A. Dijksman, Robert P. Behringer, and Gary Froyland.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres. Soft Matter, 11:2157-2173, 2015. Submitted version
Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article

Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1(2):249-278, 2014. Journal Article
Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl.

A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article

Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A computational method to extract macroscopic variables and their dynamics in multiscale systems. SIAM Journal on Applied Dynamical Systems, 13(4):1816-1846, 2014. Journal Article
Gary Froyland, Robyn M. Stuart, and Erik van Sebille.

How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: How well connected is the surface of the global ocean? Chaos, 24:033126, 2014. Journal Article
David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.

Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys Rev E, 89:032205, 2014. Journal Article.
Gary Froyland, Cecilia González-Tokman, and Anthony Quas.

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.

Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27:647-660, 2014 Journal Article.
Christopher Bose, Gary Froyland, Cecilia González-Tokman, and Rua Murray.

Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13(2):1010-1032, 2014. Journal Article.
Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.

An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.

Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: An Integrated Scenario-Based Approach for Robust Aircraft Routing, Crew Pairing and Re-timing. Computers and Operations Research, 45:68-86, 2014. Journal Article.
Sanjeeva Balasuriya, Gary Froyland, and Naratip Santitissadeekorn.

Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.

Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Absolute flux optimising curves of flows on a surface. Journal of Mathematical Analysis and Applications, 409:119-139, 2014. Journal Article.
Gary Froyland, Stephen Maher, and Cheng-Lung Wu.

The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.

Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: The recoverable robust tail assignment problem. Transportation Science, 48(3):351-372, 2014. Journal Article.
Gary Froyland, Philip K Pollett, and Robyn M Stuart.

A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.

Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1(1):135-162, 2014. Submitted version.
Gary Froyland.

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250:1-19, 2013. Journal Article.
David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.

Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics. Nonlinear Theory and its Applications, IEICE, Vol. E96-N(4), 2013. Submitted version.
Gary Froyland, Thorsten Huls, Gary P. Morriss, and Thomas M. Watson.

Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.

Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study. Physica D, 247(1):18-39, 2013. Journal Article.
Gary Froyland and Ognjen Stancevic.

Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version

Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Metastability, Lyapunov exponents, escape rates, and topological entropy of random dynamical systems Stochastics and Dynamics, 13(4), 2013. Proof version
Gary Froyland, Oliver Junge, and Péter Koltai.

Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Estimating long term behaviour of flows without trajectory integration: the infinitesimal generator approach. SIAM J. Numer. Anal., 51(1):223�247, 2013. Journal Article
Gary Froyland, Simon Lloyd, and Anthony Quas.
A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article

Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete and Continuous Dynamical Systems, Series A, 33(9):3835-3860, 2013. Journal Article
Erik van Sebille, Matthew H. England, and Gary Froyland.

Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie

Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Origin and evolution of the ocean garbage patches derived from surface drifter data. Environmental Research Letters, 7:044040, 2012. Submitted version and Garbage movie
Gary Froyland and Kathrin Padberg-Gehle.

Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version

Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Finite-time entropy: a probabilistic approach for measuring nonlinear stretching. Physica D, 241(19):1612-1628, 2012. Proof version
Gary Froyland, Christian Horenkamp, Vincent Rossi, Naratip Santitissadeekorn, and Alex Sen Gupta.

Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article

Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, V52-53:69-75, 2012. Journal Article
Antoinette Tordesillas, David M. Walker, Gary Froyland, Jie Zhang, and Robert P. Behringer.

Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article

Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Transition Dynamics and Magic-Number-Like Behavior of Frictional Granular Clusters. Physical Review E, 86:011306, 2012. Journal Article
Michelle Dunbar, Gary Froyland, and Cheng-Lung Wu.
Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version

Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework. Transportation Science, 46:204-216, 2012. Article in Advance version
Natashia Boland, Andreas Bley, Chris Fricke, Gary Froyland, and Renata Sotirov.
Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article

Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, Series A, 133:481-511, 2012. Journal Article
Gary Froyland, Rua Murray, and Ognjen Stancevic.
Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article

Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity, 24:2435�2463, 2011. Journal article
Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan.

Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article

Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20:043116, 2010. Journal Article
Naratip Santitissadeekorn, Gary Froyland, and Adam Monahan.

Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex Physical Review E, 82:056311, 2010. Journal Article
Gary Froyland, Simon Lloyd, and Naratip Santitissadeekorn.
Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article

Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Coherent sets for nonautonomous dynamical systems. Physica D, 239:1527--1541, 2010. Journal Article
Gary Froyland and Ognjen Stancevic.
Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article

Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - Series A, 14:457--472, 2010. Journal Article
Andreas Bley, Natashia Boland, Chris Fricke, and Gary Froyland.
A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article

Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers and Operations Research, 37:1641-1647, 2010. Journal Article
Gary Froyland, Simon Lloyd, and Anthony Quas.
Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory and Dynamical Systems, 30:729-756, 2010. Journal Article
Michael Dellnitz, Gary Froyland, Christian Horenkamp, Kathrin Padberg-Gehle, and Alex Sen Gupta.
Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article

Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16:655-664, 2009. Journal Article
Gary Froyland and Kathrin Padberg.
Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article

Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Almost-invariant sets and invariant manifolds -- connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16):1507-1523, 2009. Journal Article
Michael Dellnitz, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article

Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: On the Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen, 32(1):47--60, 2009. Journal Article
Natashia Boland, Irina Dumitrescu, Gary Froyland, and Ambros M. Gleixner.
LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article

Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: LP-Based Disaggregation Approaches to Solving the Open Pit Mining Production Scheduling Problem with Block Processing Selectivity. Computers and Operations Research, 36(4):1064--1089, 2009. Journal article
Dalia Terhesiu and Gary Froyland.
Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.

Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure for expanding maps. Nonlinearity, 21:1953--1966, 2008. Journal Article.
Gary Froyland.
Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article

Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps. Physica D, 237(6):840--853, 2008. Abstract | Journal Article
Gary Froyland, Thorsten Koch, Nicole Megow, Emily Duane, and Howard Wren.
Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article

Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Optimizing the landside operation of a container terminal. OR Spectrum, 30:53-75, 2008. Abstract | Journal Article
Gary Froyland, Rua Murray, and Dalia Terhesiu.
Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E, 76:036702, 2007. Abstract | Journal Article | MathReviews doc
Gary Froyland, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily

Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Detecting coherent oceanic structures via transfer operators. Physical Review Letters, 98:224503, 2007. Abstract | Journal Article | Media Report in Science Daily
Gary Froyland.

On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps . Discrete and Continuous Dynamical Systems, Series A, 17(3):671-689, 2007. Abstract | Journal Article | MathReviews doc
Gary Froyland.
Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc

Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Statistically optimal almost-invariant sets. Physica D, 200:205-219, 2005. Abstract | Journal Article | MathReviews doc
Gary Froyland and Michael Dellnitz.
Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc

David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Detecting and locating near-optimal almost-invariant sets and cycles. SIAM J. Sci. Comput., 24(6): 1839-1863, 2003. Abstract | Journal Article | MathReviews doc
David Walker, Gary Froyland, Kevin Judd, and Alistair Mees.
Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc

Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Controllers for nonlinear systems using normal forms. Internat. J. Bifur. Chaos Appl. Sci. Engrg, 13(2):459-465, 2003. Abstract | Journal Article | MathReviews doc
Gary Froyland, Oliver Junge, and Gunter Ochs.
Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Rigorous computation of topological entropy with respect to a finite partition. Physica D, 154(1-2):68-84, 2001. Abstract | Journal Article | MathReviews doc
Gary Froyland and Kazuyuki Aihara.
Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Estimating statistics of neuronal dynamics via Markov chains. Biological Cybernetics, 84(1):31-40, 2001. Abstract | Journal Article
Michael Dellnitz, Gary Froyland, and Stefan Sertl.
On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 13(4):1171-1188, 2000. Abstract | Journal Article | MathReviews doc
Gary Froyland and Kazuyuki Aihara.
Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Rigorous numerical estimation of Lyapunov exponents and invariant measures of iterated function systems and random matrix products. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(1):103-122, 2000. Abstract | Journal Article | MathReviews doc
Gary Froyland.
Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Ulam's method for random interval maps. Nonlinearity, 12:1029-1052, 1999. Abstract | Journal Article | MathReviews doc
Gary Froyland.
Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc

Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Using Ulam's method to calculate entropy and other dynamical invariants. Nonlinearity, 12(1):79-101, 1999. Abstract | Journal Article | MathReviews doc
Liang-yue Cao, Alistair I. Mees, Kevin Judd and Gary Froyland.
Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)

Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Determining the minimum embedding dimensions of input-output time series data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8(7):1491-1504, 1998. Abstract | Journal Article (tar file with .ps file and figures)
Gary Froyland.
Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Approximating physical invariant measures of mixing dynamical systems in higher dimensions. Nonlinear Anal., 32(7):831-360, 1998. Abstract | Journal Article | MathReviews doc
Gary Froyland.
Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc

Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Computer-assisted bounds for the rate of decay of correlations. Comm. Math. Phys., 189(1):237-257, 1997. Abstract | Journal Article | MathReviews doc
Gary Froyland.
Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc

Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Finite approximation of Sinai-Bowen-Ruelle measures of Anosov systems in two dimensions. Random Comput. Dynam., 3(4):251-264, 1995. Abstract | pdf file | MathReviews doc
Gary Froyland, Kevin Judd, Alistair I. Mees, Kenji Murao, and David Watson.

Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article

Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Constructing invariant measures from data. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5(4):1181-1192, 1995. Abstract | Journal Article
Gary Froyland, Kevin Judd, and Alistair I. Mees.
Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc: Estimation of Lyapunov exponents of dynamical systems using a spatial average. Phys. Rev. E, 51(4):2844-2855, 1995. Abstract | Journal Article | MathReviews doc

Refereed Conference Proceedings & Other Journals

Bharat Monga, Gary Froyland, and Jeff Moehlis.

Synchronizing and Desynchronizing Neural Populations through Phase Distribution Control. Proceedings of the 2018 American Control Conference, June 27-29, Milwaukee, pp. 2808--2813, 2018. Conference article

Sebastian Pucilowski, Antoinette Tordesillas, and Gary Froyland.

Self-organization in the localised failure regime: metastable attractors and their implications on force chain functionality, in Proceedings of Powders and Grains 2017, 3-7 July 2017, EPJ Web of Conferences, 140:10007, 2017. Conference Article

Amirah Rahman and Gary Froyland.

Freight train scheduling on a single line corridor, In AIP Conference Proceedings, STATISTICS AND OPERATIONAL RESEARCH INTERNATIONAL CONFERENCE (SORIC 2013), 1613:159-168, 2014. Conference Article

Gary Froyland, Antoinette Tordesillas, and David M. Walker.

Global Markov modelling and analysis of the dynamics of granular deformation and flow dynamics, In AIP Conference Proceedings (Powders and Grains, Sydney, 2013), 1542:563-566, 2013. Submitted version

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Similarity Networks of the Functional Evolution of Cycles in Structural Networks, In Proceedings, International Symposium on Nonlinear Theory and its Applications (NOLTA), Majorca, Spain, pages 502--505, 2012. Submitted version

Don Weatherburn, Gary Froyland, Steve Moffatt, and Simon Corben.

Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version

Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Synchronizing and Desynchronizing Neural Populations through Phase Distribution Control. Proceedings of the 2018 American Control Conference, June 27-29, Milwaukee, pp. 2808--2813, 2018. Conference article
Sebastian Pucilowski, Antoinette Tordesillas, and Gary Froyland.

Self-organization in the localised failure regime: metastable attractors and their implications on force chain functionality, in Proceedings of Powders and Grains 2017, 3-7 July 2017, EPJ Web of Conferences, 140:10007, 2017. Conference Article

Amirah Rahman and Gary Froyland.

Freight train scheduling on a single line corridor, In AIP Conference Proceedings, STATISTICS AND OPERATIONAL RESEARCH INTERNATIONAL CONFERENCE (SORIC 2013), 1613:159-168, 2014. Conference Article

Gary Froyland, Antoinette Tordesillas, and David M. Walker.

Global Markov modelling and analysis of the dynamics of granular deformation and flow dynamics, In AIP Conference Proceedings (Powders and Grains, Sydney, 2013), 1542:563-566, 2013. Submitted version

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Similarity Networks of the Functional Evolution of Cycles in Structural Networks, In Proceedings, International Symposium on Nonlinear Theory and its Applications (NOLTA), Majorca, Spain, pages 502--505, 2012. Submitted version

Don Weatherburn, Gary Froyland, Steve Moffatt, and Simon Corben.

Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version

Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Self-organization in the localised failure regime: metastable attractors and their implications on force chain functionality, in Proceedings of Powders and Grains 2017, 3-7 July 2017, EPJ Web of Conferences, 140:10007, 2017. Conference Article
Amirah Rahman and Gary Froyland.

Freight train scheduling on a single line corridor, In AIP Conference Proceedings, STATISTICS AND OPERATIONAL RESEARCH INTERNATIONAL CONFERENCE (SORIC 2013), 1613:159-168, 2014. Conference Article

Gary Froyland, Antoinette Tordesillas, and David M. Walker.

Global Markov modelling and analysis of the dynamics of granular deformation and flow dynamics, In AIP Conference Proceedings (Powders and Grains, Sydney, 2013), 1542:563-566, 2013. Submitted version

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Similarity Networks of the Functional Evolution of Cycles in Structural Networks, In Proceedings, International Symposium on Nonlinear Theory and its Applications (NOLTA), Majorca, Spain, pages 502--505, 2012. Submitted version

Don Weatherburn, Gary Froyland, Steve Moffatt, and Simon Corben.

Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version

Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Freight train scheduling on a single line corridor, In AIP Conference Proceedings, STATISTICS AND OPERATIONAL RESEARCH INTERNATIONAL CONFERENCE (SORIC 2013), 1613:159-168, 2014. Conference Article
Gary Froyland, Antoinette Tordesillas, and David M. Walker.

Global Markov modelling and analysis of the dynamics of granular deformation and flow dynamics, In AIP Conference Proceedings (Powders and Grains, Sydney, 2013), 1542:563-566, 2013. Submitted version

David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Similarity Networks of the Functional Evolution of Cycles in Structural Networks, In Proceedings, International Symposium on Nonlinear Theory and its Applications (NOLTA), Majorca, Spain, pages 502--505, 2012. Submitted version

Don Weatherburn, Gary Froyland, Steve Moffatt, and Simon Corben.

Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version

Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Global Markov modelling and analysis of the dynamics of granular deformation and flow dynamics, In AIP Conference Proceedings (Powders and Grains, Sydney, 2013), 1542:563-566, 2013. Submitted version
David M. Walker, Antoinette Tordesillas, and Gary Froyland.

Similarity Networks of the Functional Evolution of Cycles in Structural Networks, In Proceedings, International Symposium on Nonlinear Theory and its Applications (NOLTA), Majorca, Spain, pages 502--505, 2012. Submitted version

Don Weatherburn, Gary Froyland, Steve Moffatt, and Simon Corben.

Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version

Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Similarity Networks of the Functional Evolution of Cycles in Structural Networks, In Proceedings, International Symposium on Nonlinear Theory and its Applications (NOLTA), Majorca, Spain, pages 502--505, 2012. Submitted version
Don Weatherburn, Gary Froyland, Steve Moffatt, and Simon Corben.

Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version

Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Prison populations and correctional outlays: The effect of reducing re-imprisonment. Crime and Justice Bulletin NSW. Volume 138, 2009. Submitted version
Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland.
Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version

Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Clique-based facets for the precedence constrained knapsack problem. In Proceedings of the 9th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2009), Rolduc, The Netherlands, (eds. C. Stein, M. Uetz, and T. Vredeveld), pages 259-269, 2009. Submitted version
Gary Froyland, Marcel Schwalb, Kathrin Padberg, and Michael Dellnitz.
A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version

Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: A transfer operator based numerical investigation of coherent structures in three-dimensional Southern ocean circulation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, September 2008, pages 313-316, 2008. Submitted version
Gary Froyland, Merab Menabde, Peter Stone, and Dave Hodson.
The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: The Value of Additional Drilling to Open Pit Mining Projects. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 169-176, Perth, November 2004. Accepted version
NOTE THAT THERE ARE SEVERAL CRUCIAL MISPRINTS IN THE RE-TYPESET AND REPRINTED CHAPTER IN ``ADVANCES IN STRATEGIC MINE PLANNING'', SPRINGER 2018.
Merab Menabde, Gary Froyland, Peter Stone, and Gavin Yeates.
Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article

Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Mining Schedule Optimisation for Conditionally Simulated Orebodies. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 357-342, Perth, November 2004. Reprinted article
Peter Stone, Gary Froyland, Merab Menabde, Brian Law, Reza Pasyar, and Peter Monkhouse.
Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article

Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Blasor - Blended Iron Ore Mine Planning Optimisation at Yandi. In Proceedings of Orebody Modelling and Strategic Mine Planning - Uncertainty and Risk Management, pages 285-288, Perth, November 2004. Reprinted article
Gary Froyland.
Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)

Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Markov modelling of random dynamical systems. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (780K)
Michael Dellnitz, Gary Froyland, and Stefan Sertl.
A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)

Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: A conjecture on the existence of isolated eigenvalues of the Perron-Frobenius operator. In Proceedings of Equadiff 99, Berlin, Germany, August 1999. Abstract | postscript file (???K)
Gary Froyland and Kazuyuki Aihara.
Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)

Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Statistical analysis of a randomly stimulated neuron. In Proceedings of the 1998 International Conference on Neural Information Processing, Kitakyushu, Japan, October 1998. volume 3, pages 1442-1445, 1998. Abstract | postscript file (560K)
Gary Froyland and Kazuyuki Aihara.
Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)

Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Ulam formulae for random and forced systems In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 2, pages 623-626, 1998. Abstract | postscript file (85K)
Gary Froyland.
Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)

Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Finding slowly decaying observables. In Proceedings of the 1998 International Symposium on Nonlinear Theory and its Applications, Crans-Montana, Switzerland, September 1998, volume 1, pages 183-186, 1998. Abstract | postscript file (120K)
Gary Froyland.
Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)

Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Mixing invariant densities. In Proceedings of the 1998 International Symposium on Artificial Life and Robotics, Beppu, Oita, Japan, January 1998. volume 1, pages 346-349, 1998. Abstract | postscript file (120K)
Gary Froyland.
Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)

Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Computing physical invariant measures. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1129-1132, 1997. Abstract | postscript file (135K)
Liangyue Cao, Alistair Mees, Kevin Judd, and Gary Froyland.
Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract

Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Identification of variable relations from multivariate chaotic time series data. In Proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1997, volume 2, pages 1305-1308, 1997. Abstract
Gary Froyland.
Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version

Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Abstract of Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. Bull. Austral. Math. Soc., 56(1):157-159, 1997. Text version
Gary Froyland, Kevin Judd, Alistair I. Mees, and Kenji Murao.
Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)

Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Lyapunov exponents and triangulations. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 281-286, 1993. Abstract | postscript file (50K)
Alistair I. Mees, Kenji Murao, Kevin Judd, and Gary Froyland.
Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.: Triangulations on tori and density estimation. In Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, December 1993, volume 1, pages 275-280, 1993.

Other Publications

Andreas Bley, Natashia Boland, Gary Froyland, and Mark Zuckerberg.
Solving mixed integer nonlinear programming problems for mine production planning with stockpiling. Archived. Archived version.

S. Mehrdad Heidari and Gary Froyland.

On quantifying the space of uncertainty of stochastic simulations. Submitted. Submitted version

Natashia Boland, Irina Dumitrescu, and Gary Froyland.
A Multistage Stochastic Programming Approach to Open Pit Mining Production Scheduling with Uncertain Geology. Submitted. Archived copy

Gary Froyland, Thorsten Koch, Nicole Megow, Andre Costa, and Emily Duane
Finding the Strategic Corridor. Final report on the pilot project regarding control and optimising of the new automated RMG based road/rail exchange area at Patrick�s Port Botany container terminal. October 2005.

Gary Froyland.
On estimating invariant measures and Lyapunov exponents for iid compositions of maps. Technical report, 1998. Abstract | pdf file

Gary Froyland.
Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)

Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: Solving mixed integer nonlinear programming problems for mine production planning with stockpiling. Archived. Archived version.
S. Mehrdad Heidari and Gary Froyland.

On quantifying the space of uncertainty of stochastic simulations. Submitted. Submitted version

Natashia Boland, Irina Dumitrescu, and Gary Froyland.
A Multistage Stochastic Programming Approach to Open Pit Mining Production Scheduling with Uncertain Geology. Submitted. Archived copy

Gary Froyland, Thorsten Koch, Nicole Megow, Andre Costa, and Emily Duane
Finding the Strategic Corridor. Final report on the pilot project regarding control and optimising of the new automated RMG based road/rail exchange area at Patrick�s Port Botany container terminal. October 2005.

Gary Froyland.
On estimating invariant measures and Lyapunov exponents for iid compositions of maps. Technical report, 1998. Abstract | pdf file

Gary Froyland.
Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)

Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: On quantifying the space of uncertainty of stochastic simulations. Submitted. Submitted version
Natashia Boland, Irina Dumitrescu, and Gary Froyland.
A Multistage Stochastic Programming Approach to Open Pit Mining Production Scheduling with Uncertain Geology. Submitted. Archived copy

Gary Froyland, Thorsten Koch, Nicole Megow, Andre Costa, and Emily Duane
Finding the Strategic Corridor. Final report on the pilot project regarding control and optimising of the new automated RMG based road/rail exchange area at Patrick�s Port Botany container terminal. October 2005.

Gary Froyland.
On estimating invariant measures and Lyapunov exponents for iid compositions of maps. Technical report, 1998. Abstract | pdf file

Gary Froyland.
Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)

Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: A Multistage Stochastic Programming Approach to Open Pit Mining Production Scheduling with Uncertain Geology. Submitted. Archived copy
Gary Froyland, Thorsten Koch, Nicole Megow, Andre Costa, and Emily Duane
Finding the Strategic Corridor. Final report on the pilot project regarding control and optimising of the new automated RMG based road/rail exchange area at Patrick�s Port Botany container terminal. October 2005.

Gary Froyland.
On estimating invariant measures and Lyapunov exponents for iid compositions of maps. Technical report, 1998. Abstract | pdf file

Gary Froyland.
Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)

Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: Finding the Strategic Corridor. Final report on the pilot project regarding control and optimising of the new automated RMG based road/rail exchange area at Patrick�s Port Botany container terminal. October 2005.
Gary Froyland.
On estimating invariant measures and Lyapunov exponents for iid compositions of maps. Technical report, 1998. Abstract | pdf file

Gary Froyland.
Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)

Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: On estimating invariant measures and Lyapunov exponents for iid compositions of maps. Technical report, 1998. Abstract | pdf file
Gary Froyland.
Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)

Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: Estimating Physical Invariant Measures and Space Averages of Dynamical Systems Indicators. PhD thesis. The University of Western Australia. Abstract (text) | Contents page (text) | Entire thesis (pdf)
Gary Froyland.
Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.

Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: Notes I wrote in the mid-90's for a short course on Ergodic theory of differentiable dynamical systems.
Gary Froyland.
Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.: Chaos, shadowing, and computer orbits of dynamical systems. Honours thesis. The University of Queensland, Australia.

Gary Froyland

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