Select Publications

Journal articles

Roberts JAG; Saito A; Vivaldi F, 2021, 'Critical curves of a piecewise linear map', Chaos, vol. 31, pp. 073134 - 073134, http://dx.doi.org/10.1063/5.0054334

Roberts JAG; Tran DT, 2019, 'Algebraic entropy of (integrable) lattice equations and their reductions', Nonlinearity, vol. 32, pp. 622 - 653, http://dx.doi.org/10.1088/1361-6544/aaecda

Tran DT; Roberts JAG, 2019, 'Linear degree growth in lattice equations', Journal of Computational Dynamics, vol. 6, pp. 449 - 467, http://dx.doi.org/10.3934/jcd.2019023

Baake M; Roberts JAG; Yassawi R, 2018, 'Reversing and extended symmetries of shift spaces', Discrete and Continuous Dynamical Systems- Series A, vol. 38, pp. 835 - 866, http://dx.doi.org/10.3934/dcds.2018036

Evripidou CA; Quispel GRW; Roberts JAG, 2018, 'Poisson structures for difference equations', Journal of Physics A: Mathematical and Theoretical, vol. 51, http://dx.doi.org/10.1088/1751-8121/aae746

Mahomed FM; Roberts JAG, 2015, 'Characterization of Hamiltonian symmetries and their first integrals', International Journal of Non-Linear Mechanics, vol. 74, pp. 84 - 91, http://dx.doi.org/10.1016/j.ijnonlinmec.2015.04.005

Roberts JAG; Vivaldi F, 2015, 'Arithmetic exponents in piecewise-affine planar maps', Physica D: Nonlinear Phenomena, vol. 298-299, pp. 1 - 12, http://dx.doi.org/10.1016/j.physd.2015.01.007

Roberts JAG; Jogia D, 2015, 'Birational maps that send biquadratic curves to biquadratic curves', Journal of Physics A: Mathematical and Theoretical, vol. 48, http://dx.doi.org/10.1088/1751-8113/48/8/08FT02

Roberts JAG; Tran DT, 2015, 'Signatures over finite fields of growth properties for lattice equations', Journal of Physics A: Mathematical and Theoretical, vol. 48, http://dx.doi.org/10.1088/1751-8113/48/8/085201

Baake M; Neumarker N; Roberts JA, 2013, 'Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices', Discrete and Continuous Dynamical Systems, vol. 33, pp. 527 - 553, http://dx.doi.org/10.3934/dcds.2013.33.527

Ormerod JT; Quispel GR; Roberts JA, 2012, 'Book Review- Discrete Integrable Systems: QRT Mappings and Elliptic Surfaces', Discrete Integrable Systems: QRT Mappings and Elliptic Surfaces

Neumarker N; Roberts JA; Vivaldi F, 2012, 'Distribution of periodic orbits for the Casati-Prosen map on rational lattices', Physica D - Nonlinear Phenomena, vol. 241, pp. 360 - 371, http://dx.doi.org/10.1016/j.physd.2011.10.006

Roberts JA; Vivaldi F, 2009, 'A combinatorial model for reversible rational maps over finite fields', Nonlinearity, vol. 22, pp. 1965 - 1982, http://dx.doi.org/10.1088/0951-7715/22/8/011

Pettigrew JA; Roberts JA, 2008, 'Characterizing singular curves in parametrized families of biquadratics', JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 41, pp. 115203-1 - 115203-28, http://dx.doi.org/10.1088/1751-8113/41/11/115203

Baake M; Roberts JA; Weiss A, 2008, 'Periodic orbits of linear endomorphisms on the 2-torus and its lattices', Nonlinearity, vol. 21, pp. 2427 - 2446, http://dx.doi.org/10.1088/0951-7715/21/10/012

Jogia DM; Roberts JA; Vivaldi F, 2006, 'An algebraic geometric approach to integrable maps of the plane', Journal of Physics A - Mathematical and General, vol. 39, pp. 1133 - 1149, http://dx.doi.org/10.1088/0305-4470/39/5/008

Roberts JA; Quispel GR, 2006, 'Creating and relating three-dimensional integrable maps', Journal of Physics A - Mathematical and General, vol. 39, pp. L605 - L615, http://dx.doi.org/10.1088/0305-4470/39/42/L03

Baake M; Roberts JA, 2006, 'The structure of reversing symmetry groups', Bulletin of the Australian Mathematical Society, vol. 73, pp. 445 - 459, http://dx.doi.org/10.1017/S0004972700035450

Quispel GR; Capel HW; Roberts JA, 2005, 'Duality for discrete integrable systems', Journal of Physics A - Mathematical and General, vol. 38, pp. 3965 - 3980, http://dx.doi.org/10.1088/0305-4470/38/18/007

Roberts JA; Vivaldi F, 2005, 'Signature of time-reversal symmetry in polynomial automorphisms over finite fields', Nonlinearity, vol. 18, pp. 2171 - 2192, http://dx.doi.org/10.1088/0951-7715/18/5/015

Baake M; Roberts JA, 2005, 'Symmetries and reversing symmetries of polynomial automorphisms of the plane', Nonlinearity, vol. 18, pp. 791 - 816, http://dx.doi.org/10.1088/0951-7715/18/2/017

Roberts JAG; Vivaldi F, 2003, 'Erratum: Arithmetical method to detect integrability in maps (Phys. Rev. Lett. (2003) 90 (034102))', Physical Review Letters, vol. 90

Roberts JAG; Vivaldi F, 2003, 'Publisher’s Note: Arithmetical Method to Detect Integrability in Maps [Phys. Rev. Lett. 90, 034102 (2003)]', Physical Review Letters, vol. 90, http://dx.doi.org/10.1103/PhysRevLett.90.079902

Roberts JA; Vivaldi F, 2003, 'Arithmetical method to detect integrability in maps', Physical Review Letters, vol. 90, pp. 4, http://dx.doi.org/10.1103/PhysRevLett.90.034102

Iatrou A; Roberts JA, 2003, 'Integrable mappings of the plane preserving biquadratic invariant curves III', Physica A - Statistical Mechanics and Its Applications, vol. 326, pp. 400 - 411, http://dx.doi.org/10.1016/S0378-4371(03)00268-1

Roberts JA; Baake M, 2003, 'Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form', Physica A - Statistical Mechanics and Its Applications, vol. 317, pp. 95 - 112, http://dx.doi.org/10.1016/S0378-4371(02)01321-3

Roberts JA; Jogia DM; Vivaldi F, 2003, 'The Hasse-Weil bound and integrability detection in rational maps', Journal of Nonlinear Mathematical Physics, vol. 10, pp. 166 - 180, http://dx.doi.org/10.2991/jnmp.2003.10.s2.14

Roberts JAG; Jogia D; Vivaldi F, 2003, 'The Hasse-Weil Bound and Integrability Detection in Rational Maps', Journal of Nonlinear Mathematical Physics, vol. 10, pp. 166 - 166, http://dx.doi.org/10.2991/jnmp.2003.10.s2.15

Iatrou A; Roberts JAG, 2002, 'Integrable mappings of the plane preserving biquadratic invariant curves II (vol 15, pg 459, 2002)', NONLINEARITY, vol. 15, pp. 955 - 955, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000175697700028&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Iatrou A; Roberts JA, 2002, 'Integrable mappings of the plane preserving biquadratic invariant curves II', Nonlinearity, vol. 15, pp. 459 - 489, http://dx.doi.org/10.1088/0951-7715/15/2/313

Roberts JA; Iatrou A; Quispel GR, 2002, 'Interchanging parameters and integrals in dynamical systems: the mapping case', Journal of Physics A - Mathematical and General, vol. 35, pp. 2309 - 2325, http://dx.doi.org/10.1088/0305-4470/35/9/318

Iatrou A; Roberts JAG, 2001, 'Integrable mappings of the plane preserving biquadratic invariant curves', Journal of Physics A: Mathematical and General, vol. 34, pp. 6617 - 6636, http://dx.doi.org/10.1088/0305-4470/34/34/308

Baake M; Roberts JAG, 2001, 'Symmetries and reversing symmetries of toral automorphisms', Nonlinearity, vol. 14, http://dx.doi.org/10.1088/0951-7715/14/4/201

Pettigrew JA; Roberts JA; Vivaldi F, 2001, 'Complexity of regular invertible p-adic motions', Chaos, vol. 11, pp. 849 - 857, http://dx.doi.org/10.1063/1.1423334

Lamb JSW; Roberts JAG, 1998, 'Time-reversal symmetry in dynamical systems: A survey', Physica D: Nonlinear Phenomena, vol. 112, pp. 1 - 39, http://dx.doi.org/10.1016/S0167-2789(97)00199-1

Baake M; Roberts JAG, 1997, 'Reversing symmetry group of Gl(2, ℤ) and PGl(2, ℤ) matrices with connections to cat maps and trace maps', Journal of Physics A: Mathematical and General, vol. 30, pp. 1549 - 1573, http://dx.doi.org/10.1088/0305-4470/30/5/020

Roberts JAG, 1996, 'Escaping orbits in trace maps', Physica A: Statistical Mechanics and its Applications, vol. 228, pp. 295 - 325, http://dx.doi.org/10.1016/0378-4371(95)00428-9

Roberts JAG; Lamb JSW, 1995, 'Self-similarity of period-doubling branching in 3-D reversible mappings', Physica D: Nonlinear Phenomena, vol. 82, pp. 317 - 332, http://dx.doi.org/10.1016/0167-2789(94)00229-J

Roberts JAG; Baake M, 1994, 'Trace maps as 3D reversible dynamical systems with an invariant', Journal of Statistical Physics, vol. 74, pp. 829 - 888, http://dx.doi.org/10.1007/BF02188581

Lamb JSW; Roberts JAG; Capel HW, 1993, 'Conditions for local (reversing) symmetries in dynamical systems', Physica A: Statistical Mechanics and its Applications, vol. 197, pp. 379 - 422, http://dx.doi.org/10.1016/0378-4371(93)90592-R

Roberts JAG; Capel HW, 1992, 'Area preserving mappings that are not reversible', Physics Letters A, vol. 162, pp. 243 - 248, http://dx.doi.org/10.1016/0375-9601(92)90441-N

Roberts JAG; Quispel GRW, 1992, 'Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems', Physics Reports, vol. 216, pp. 63 - 177, http://dx.doi.org/10.1016/0370-1573(92)90163-T

Roberts JAG, 1990, 'Order and chaos in reversible dynamical systems', Bulletin of the Australian Mathematical Society, vol. 42, pp. 527 - 528, http://dx.doi.org/10.1017/s0004972700028707

Quispel GRW; Roberts JAG, 1989, 'Conservative and dissipative behaviour in reversible dynamical systems', Physics Letters A, vol. 135, pp. 337 - 342, http://dx.doi.org/10.1016/0375-9601(89)90004-2

Quispel GRW; Roberts JAG; Thompson CJ, 1989, 'Integrable mappings and soliton equations II', Physica D: Nonlinear Phenomena, vol. 34, pp. 183 - 192, http://dx.doi.org/10.1016/0167-2789(89)90233-9

Quispel GRW; Roberts JAG, 1988, 'Reversible mappings of the plane', Physics Letters A, vol. 132, pp. 161 - 163, http://dx.doi.org/10.1016/0375-9601(88)90274-5

Roberts JAG; Thompson CJ, 1988, 'Dynamics of the classical heisenberg spin chain', Journal of Physics A: Mathematical and General, vol. 21, pp. 1769 - 1780, http://dx.doi.org/10.1088/0305-4470/21/8/013

Quispel GRW; Roberts JAG; Thompson CJ, 1988, 'Integrable mappings and soliton equations', Physics Letters A, vol. 126, pp. 419 - 421, http://dx.doi.org/10.1016/0375-9601(88)90803-1


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