**Office:**Room 3065, Red Centre**Phone:**+61 2 9385 7052**Email:**- Jag.Roberts@unsw.edu.au
**Mail:**
School of Mathematics and Statistics

UNSW Australia

Sydney NSW 2052, Australia

Nonlinear dynamical systems, with particular interests in the following topics (and their interrelation):

- G.R.W. Quispel, J.A.G. Roberts and C.J. Thompson, Integrable mappings and
soliton equations II,
*Physica D***34**(1989) 183-192. - A. Iatrou and J.A.G. Roberts,
Integrable mappings of the plane preserving biquadratic invariant curves II,
*Nonlinearity***15**(2002) 459-489. PDF version - J.A.G. Roberts, A. Iatrou and G.R.W. Quispel, Interchanging parameters and
integrals in dynamical systems: the mapping case.
*J. Phys. A: Math. Gen.***35**(2002) 2309-2325. PDF version - J.A.G. Roberts and F. Vivaldi,
Arithmetical method to detect integrability in maps,
*Phys. Rev. Lett.***90**(2003) 034102. PDF version - G.R.W. Quispel, H.W. Capel and J.A.G. Roberts, Duality for discrete integrable systems,
*J. Phys. A: Math. Gen.***38**(2005) 3965-3980. PDF version - D. Jogia, J.A.G. Roberts and F. Vivaldi, An algebraic geometric approach to
integrable maps of the plane,
*J. Phys. A: Math. Gen.***39**(2006) 1133-1149. PDF version - J.A.G. Roberts and G.R.W. Quispel,
Creating and relating 3-dimensional integrable maps,
*J. Phys. A: Math. Gen.***39**(2006) L605-L615. PDF version - J. Pettigrew and J.A.G. Roberts,
Characterizing singular curves in parametrized families of biquadratics,
*J. Phys. A: Math. Theor.***41**(2008) 115203. PDF version

- J.A.G. Roberts and G.R.W. Quispel, Chaos and time-reversal symmetry. Order
and chaos in reversible dynamical systems,
*Phys. Rep.***216**(1992) 63-177. - J.A.G. Roberts and J.S.W. Lamb, Self-similarity of period-doubling
branching in 3D reversible mappings,
*Physica D***82**(1995) 317-332.PDF version - J.S.W. Lamb and J.A.G. Roberts, Time-reversal symmetry in dynamical
systems: a survey,
*Physica D***112**(1998) 1-39.PDF version - M.Baake and J.A.G. Roberts,
Symmetries and reversing symmetries of polynomial automorphisms of the plane,
*Nonlinearity***18**(2005) 791-816. PDF version - J.A.G. Roberts and F. Vivaldi,
Signature of time-reversal symmetry in polynomial automorphisms over finite fields,
*Nonlinearity***18**(2005) 2171-2192. PDF version - M.Baake and J.A.G. Roberts,
The structure of reversing symmetry groups,
*Bull. Austral. Math. Soc.***73**(2006) 445-459. PDF version

- J.A.G. Roberts and M. Baake, Trace maps as 3D reversible dynamical systems
with an invariant,
*J. Stat. Phys.***74**(1994) 829-888. PDF version - J.A.G. Roberts, Escaping orbits in trace maps,
*Physica A***228**(1996) 295-325. PDF version - M. Baake and J.A.G. Roberts, Reversing symmetry group of GL(2,Z) and
PGL(2,Z) matrices with connections to cat maps and trace maps,
*J. Phys. A: Math. Gen.***30**(1997) 1549-1573. PDF version - M.Baake and J.A.G. Roberts,
Symmetries and reversing symmetries of toral automorphisms,
*Nonlinearity***14**(2001) R1-24. PDF version

- J. Pettigrew, J.A.G. Roberts and F. Vivaldi,
Complexity of regular invertible p-adic motions,
*Chaos***11**(2001) 849-857. PDF version - J.A.G. Roberts and F. Vivaldi,
Arithmetical method to detect integrability in maps,
*Phys. Rev. Lett.***90**(2003) 034102. PDF version - J.A.G. Roberts, D. Jogia and F. Vivaldi,
The Hasse-Weil bound and integrability detection in rational maps,
*J. Nonlinear Math. Phys.***10**(2003) 166-180. PDF version - J.A.G. Roberts and F. Vivaldi,
Signature of time-reversal symmetry in polynomial automorphisms over finite fields,
*Nonlinearity***18**(2005) 2171-2192. PDF version - M.Baake, J.A.G. Roberts and A. Weiss,
Periodic orbits of linear endomorphisms on the 2-torus and its lattices,
*Nonlinearity***21**(2008) 2427-2446. PDF version - J.A.G. Roberts and F. Vivaldi,
A combinatorial model for reversible rational maps over finite fields,
*Nonlinearity***22**(2009) 1965-1982. PDF version - J.A.G. Roberts, Order and symmetry in birational difference equations and their signatures over finite phase spaces, Proceedings of the Workshop Future Directions in Difference Equations, Conference Collection 69, Univ. Vigo, Serv. Publ., Vigo, (2011) pp. 213-221. PDF version
- N.Neumaerker, J.A.G. Roberts and F. Vivaldi,
Distribution of periodic orbits for the Casati-Prosen
map on rational lattices,
*Physica D***241**(2012) 360-371. PDF version - M.Baake, N.Neumaerker and J.A.G. Roberts,
Orbit structure and (reversing) symmetries of toral
endomorphisms on rational lattices,
*Discrete and Continuous Dynamical Systems***33**(2013) 527-553. PDF version

- Dinh Tran [integrable systems], 2016-17
- Alina Ostafe [arithmetic dynamics] [UNSW VC Postdoc], 10/2013-
- Dinh Tran [integrable systems], 2011-13
- Natascha Neumaerker [arithmetic dynamics], 2009-10
- Danesh Jogia [integrable systems], 2008

I very much enjoy supervising (good!) postgraduate students - formulating ideas and projects and seeing them through to fruition in papers and theses. Please feel free to contact me if your research interests match mine.

Current and recent students:- Tim Siu,
*Arithmetic dynamics and integrable systems*, PhD, 2014- - Natascha Neumaerker,
*The arithmetic structure of discrete dynamical systems on the torus*, PhD, 2008-12 (PhD granted by University of Bielefeld; co-supervision with Prof M Baake) - Jim Pettigrew,
*Characterising singular curves in parametrised families of biquadratics*, PhD, 2004-9 - Danesh Jogia,
*Algebraic aspects of integrability and reversibility in maps*, PhD, 2003-7 - Rahmi Rusin,
*A Study of Limit Cycles and Quadratic Systems*, MSc (minor thesis), 2002-3. - Apostolos Iatrou,
*Integrable Mappings of the Plane preserving biquadratic invariant curves*, PhD (La Trobe University), 2000-3. - Jim Pettigrew,
*Invertible p-adic dynamics of polynomial maps*, MSc (La Trobe University), 1999-2001.

- J.A.G. Roberts and D.T. Tran, Towards some exact results for the (vanishing) algebraic entropy of (integrable) lattice equations, preprint (2014) PDF version
- J.A.G. Roberts and D.T. Tran,
Signatures over finite fields of growth properties for lattice
equations,
*J. Phys. A: Math. Theor.***48**(2015) 085201 (20pp) PDF version - J.A.G. Roberts and D.Jogia,
Birational maps that send biquadratic curves to biquadratic curves,
*J. Phys. A: Math. Theor.***48**(2015) 08FT02 (13 pp) PDF version - J.A.G. Roberts and F. Vivaldi,
Arithmetic exponents in piecewise-affine planar maps,
*Physica D***298-299**(2015) 1-12. PDF version - F.M. Mahomed and J.A.G. Roberts,
Characterization of Hamiltonian symmetries and their first integrals,
*Int. J. Non-Linear Mechanics***74**(2015) 84-91. PDF version - M.Baake, J.A.G. Roberts and R. Yassawi, Reversing and extended symmetries of shift spaces, preprint (2016) PDF version
- J.A.G. Roberts and D.T. Tran, Algebraic entropy of (integrable) lattice equations and their reductions, preprint (2017) PDF version
- D.T. Tran and J.A.G. Roberts Linear degree growth in lattice equations, preprint (2017) PDF version

- Workshop on Algebraic, Number Theoretic and Graph Theoretic Aspects of Dynamical Systems (Sydney, February 2015) [Co-organizer]

- Dynamics Days Asia Pacific 6 (Sydney, July 2010) [Co-organizer]

- Symmetries and Integrability of Difference Equations (SIDE) VII (Melbourne, July 2006) [Co-organizer]

- MASCOS Workshop on Algebraic Dynamics (UNSW, February 2005) [Co-organizer]

Return to John Roberts Staff Page, School of Mathematics, UNSW.