By Professor John Anthony Gerard Roberts

Book Chapters

Baake M; Coons M; Grimm U; Roberts JAG; Yassawi R, 2021, 'Aperiodic Order Meets Number Theory: Origin and Structure of the Field', in MATRIX Book Series, Springer International Publishing, pp. 663 - 667, http://dx.doi.org/10.1007/978-3-030-62497-2_40

Roberts JAG, 1997, 'Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry', in Control and Chaos, Birkhäuser Boston, pp. 106 - 133, http://dx.doi.org/10.1007/978-1-4612-2446-4_7

Roberts JAG; Post T; Capel HW; Quispel GRW, 1991, 'Conservative Versus Reversible Dynamical Systems', in Research Reports in Physics, Springer Berlin Heidelberg, pp. 218 - 226, http://dx.doi.org/10.1007/978-3-642-84570-3_27

Journal articles

Hone ANW; Roberts JAG; Vanhaecke P, 2024, 'A family of integrable maps associated with the Volterra lattice', Nonlinearity, 37, pp. 095028, http://dx.doi.org/10.1088/1361-6544/ad68ba

Roberts JAG; Saito A; Vivaldi F, 2024, 'Critical curves of rotations', Indagationes Mathematicae, 35, pp. 989 - 1008, http://dx.doi.org/10.1016/j.indag.2024.02.001

Hone ANW; Roberts JAG; Vanhaecke P; Zullo F, 2024, 'Integrable maps in 4D and modified Volterra lattices', Open Communications in Nonlinear Mathematical Physics, 2024, http://dx.doi.org/10.46298/ocnmp.12491

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

Roberts JAG; Tran DT, 2019, 'Algebraic entropy of (integrable) lattice equations and their reductions', Nonlinearity, 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, 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, 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, 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, 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, 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, 48, pp. 08ft02, 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, 48, pp. 085201, 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, 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, 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, 22, pp. 1965 - 1982

Pettigrew JA; Roberts JA, 2008, 'Characterizing singular curves in parametrized families of biquadratics', JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 41, pp. 115203-1 - 115203-28

Baake M; Roberts JA; Weiss A, 2008, 'Periodic orbits of linear endomorphisms on the 2-torus and its lattices', Nonlinearity, 21, pp. 2427 - 2446

Jogia DM; Roberts JA; Vivaldi F, 2006, 'An algebraic geometric approach to integrable maps of the plane', Journal of Physics A - Mathematical and General, 39, pp. 1133 - 1149

Roberts JA; Quispel GR, 2006, 'Creating and relating three-dimensional integrable maps', Journal of Physics A - Mathematical and General, 39, pp. L605 - L615

Baake M; Roberts JA, 2006, 'The structure of reversing symmetry groups', Bulletin of the Australian Mathematical Society, 73, pp. 445 - 459

Quispel GR; Capel HW; Roberts JA, 2005, 'Duality for discrete integrable systems', Journal of Physics A - Mathematical and General, 38, pp. 3965 - 3980

Roberts JA; Vivaldi F, 2005, 'Signature of time-reversal symmetry in polynomial automorphisms over finite fields', Nonlinearity, 18, pp. 2171 - 2192

Baake M; Roberts JA, 2005, 'Symmetries and reversing symmetries of polynomial automorphisms of the plane', Nonlinearity, 18, pp. 791 - 816

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

Iatrou A; Roberts JA, 2003, 'Integrable mappings of the plane preserving biquadratic invariant curves III', Physica A - Statistical Mechanics and Its Applications, 326, pp. 400 - 411

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, 317, pp. 95 - 112

Roberts JA; Jogia DM; Vivaldi F, 2003, 'The Hasse-Weil bound and integrability detection in rational maps', Journal of Nonlinear Mathematical Physics, 10, pp. 166 - 180

Roberts JAG; Jogia D; Vivaldi F, 2003, 'The Hasse-Weil Bound and Integrability Detection in Rational Maps', Journal of Nonlinear Mathematical Physics, 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, 15, pp. 955 - 955, https://www.webofscience.com/api/gateway?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, 15, pp. 459 - 489

Roberts JA; Iatrou A; Quispel GR, 2002, 'Interchanging parameters and integrals in dynamical systems: the mapping case', Journal of Physics A - Mathematical and General, 35, pp. 2309 - 2325

Iatrou A; Roberts JAG, 2001, 'Integrable mappings of the plane preserving biquadratic invariant curves', Journal of Physics A: Mathematical and General, 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, 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, 11, pp. 849 - 857

Lamb JSW; Roberts JAG, 1998, 'Time-reversal symmetry in dynamical systems: A survey', Physica D: Nonlinear Phenomena, 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, 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, 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, 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, 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, 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, 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, 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, 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, 135, pp. 337 - 342, http://dx.doi.org/10.1016/0375-9601(89)90004-2

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