Research interests, Publications, Graduate Students, Conferences




John A G Roberts

Office:
Room 3065, Red Centre
Phone:
+61 2 9385 7052
Fax:
+61 2 9385 7123
Email:
Jag.Roberts@unsw.edu.au
Mail:
Associate Professor J A G Roberts
School of Mathematics and Statistics
The University of New South Wales
Sydney NSW 2052, Australia

Brief History

  • BSc (Hons 1), Applied Mathematics, Australian National University, 1985.
  • PhD, Mathematics, University of Melbourne, 1990.
  • Postdoctoral Fellow, Institute for Theoretical Physics, University of Amsterdam, 1990-2.
  • ARC Postdoctoral Fellowship, School of Mathematics, University of Melbourne, 1992-5.
  • Department of Mathematics, La Trobe University, 1996-2001.
  • School of Mathematics, UNSW, 2001-

    • Teaching: 1231

  • Lectures Chapter 2. PDF version
  • Lectures Chapter 5. PDF version

    Teaching: 2130

  • Lectures. PDF version
  • ExamNote PDF version

    Research Interests and Selected Papers

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

  • Integrable dynamical systems
  • Symmetry and Time-reversal symmetry
  • Dynamical systems arising from quasiperiodic physical phenomena
    • J.A.G. Roberts and M. Baake, Trace maps as 3D reversible dynamical systems with an invariant, J. Stat. Phys. 74 (1994) 829-888.
    • 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
  • Algebraic dynamics
    • 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, submitted to Nonlinearity (2008) PDF version

    Graduate Students

    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:
    • 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.

    Selected Recent Publications

    • J.A.G. Roberts and F. Vivaldi, Arithmetical method to detect integrability in maps, Phys. Rev. Lett. 90 (2003) 034102. 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
    • 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
    • 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
    • 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
    • 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 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
    • 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, submitted to Nonlinearity (2008) PDF version

    Conferences

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