ORCID Profile
0000-0002-8256-092X
Current Organisations
University of New South Wales
,
University of Melbourne
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Ordinary Differential Equations, Difference Equations and Dynamical Systems | Integrable Systems (Classical and Quantum) | Pure Mathematics | Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Number Theory And Field Theory | Dynamical Systems | Applied Mathematics | Mathematical Physics | Differential, Difference And Integral Equations | Algebra and Number Theory | Applied Mathematics not elsewhere classified |
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Mathematical Sciences | Mathematical sciences
Related Links
Publications
Integrable mappings of the plane preserving biquadratic invariant curves
Publisher: IOP Publishing
Date: 17-08-2001
Arithmetical Method to Detect Integrability in Maps
Publisher: American Physical Society (APS)
Date: 24-01-2003
Reversing and extended symmetries of shift spaces
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2018
DOI: 10.3934/DCDS.2018036
Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2013
Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems
Publisher: Elsevier BV
Date: 07-1992
Distribution of periodic orbits for the Casati–Prosen map on rational lattices
Publisher: Elsevier BV
Date: 02-0001
Arithmetic exponents in piecewise-affine planar maps
Publisher: Elsevier BV
Date: 04-2015
Periodic orbits of linear endomorphisms on the 2-torus and its lattices
Publisher: IOP Publishing
Date: 16-09-2008
Creating and relating three-dimensional integrable maps
Publisher: IOP Publishing
Date: 04-10-2006
Dynamics of the classical Heisenberg spin chain
Publisher: IOP Publishing
Date: 21-04-1988
Critical curves of a piecewise linear map
Publisher: AIP Publishing
Date: 07-2021
DOI: 10.1063/5.0054334
Abstract: We study the parameter space of a family of planar maps, which are linear on each of the right and left half-planes. We consider the set of parameters for which every orbit recurs to the boundary between half-planes. These parameters consist of algebraic curves, determined by the symbolic dynamics of the itinerary that connects boundary points. We study the algebraic and geometrical properties of these curves, in relation to such a symbolic dynamics.
Poisson structures for difference equations
Publisher: IOP Publishing
Date: 31-10-2018
The structure of reversing symmetry groups
Publisher: Cambridge University Press (CUP)
Date: 06-2006
DOI: 10.1017/S0004972700035450
Abstract: We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.
Characterizing singular curves in parametrized families of biquadratics
Publisher: IOP Publishing
Date: 04-03-2008
Self-similarity of period-doubling branching in 3-D reversible mappings
Publisher: Elsevier BV
Date: 05-1995
Escaping orbits in trace maps
Publisher: Elsevier BV
Date: 06-1996
The Extension of Integrable Mappings to Non-Commuting Variables
Publisher: Springer Science and Business Media LLC
Date: 2003
Linear degree growth in lattice equations
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2019
DOI: 10.3934/JCD.2019023
Area preserving mappings that are not reversible
Publisher: Elsevier BV
Date: 02-1992
Integrable mappings of the plane preserving biquadratic invariant curves II
Publisher: IOP Publishing
Date: 19-02-2002
Duality for discrete integrable systems
Publisher: IOP Publishing
Date: 18-04-2005
Integrable mappings of the plane preserving biquadratic invariant curves III
Publisher: Elsevier BV
Date: 08-2003
Interchanging parameters and integrals in dynamical systems: the mapping case
Publisher: IOP Publishing
Date: 25-02-2002
An algebraic geometric approach to integrable maps of the plane
Publisher: IOP Publishing
Date: 18-01-2006
Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form
Publisher: Elsevier BV
Date: 2003
A combinatorial model for reversible rational maps over finite fields
Publisher: IOP Publishing
Date: 29-06-2009
Reversible mappings of the plane
Publisher: Elsevier BV
Date: 10-1988
Complexity of regular invertiblep-adic motions
Publisher: AIP Publishing
Date: 12-2001
DOI: 10.1063/1.1423334
Abstract: We consider issues of computational complexity that arise in the study of quasi-periodic motions (Siegel discs) over the p-adic integers, where p is a prime number. These systems generate regular invertible dynamics over the integers modulo p(k), for all k, and the main questions concern the computation of periods and orbit structure. For a specific family of polynomial maps, we identify conditions under which the cycle structure is determined solely by the number of Siegel discs and two integer parameters for each disc. We conjecture the minimal parametrization needed to achieve-for every odd prime p-a two-disc tessellation with maximal cycle length. We discuss the relevance of Cebotarev's density theorem to the probabilistic description of these dynamical systems. (c) 2001 American Institute of Physics.
Symmetries and reversing symmetries of polynomial automorphisms of the plane
Publisher: IOP Publishing
Date: 24-12-2014
Publisher’s Note: Arithmetical Method to Detect Integrability in Maps [Phys. Rev. Lett.PRLTAO0031-900790, 034102 (2003)]
Publisher: American Physical Society (APS)
Date: 20-02-2003
Birational maps that send biquadratic curves to biquadratic curves
Publisher: IOP Publishing
Date: 04-02-2015
Characterization of Hamiltonian symmetries and their first integrals
Publisher: Elsevier BV
Date: 09-2015
Conditions for local (reversing) symmetries in dynamical systems
Publisher: Elsevier BV
Date: 08-1993
Signatures over finite fields of growth properties for lattice equations
Publisher: IOP Publishing
Date: 30-01-2015
Algebraic entropy of (integrable) lattice equations and their reductions
Publisher: IOP Publishing
Date: 17-01-2019
Conservative and dissipative behaviour in reversible dynamical systems
Publisher: Elsevier BV
Date: 03-1989
The Hasse-Weil bound and integrability detection in rational maps
Publisher: No publisher found
Date: 2003
Symmetries and reversing symmetries of toral automorphisms
Publisher: IOP Publishing
Date: 21-05-2001
Signature of time-reversal symmetry in polynomial automorphisms over finite fields
Publisher: IOP Publishing
Date: 07-2005
Symmetries, Lagrangian Formalism and Integration of Second Order Ordinary Difference Equations
Publisher: Springer Science and Business Media LLC
Date: 2003
Time-reversal symmetry in dynamical systems: A survey
Publisher: Elsevier BV
Date: 1998
Reversing symmetry group of and matrices with connections to cat maps and trace maps
Publisher: IOP Publishing
Date: 07-03-1997
Trace maps as 3D reversible dynamical systems with an invariant
Publisher: Springer Science and Business Media LLC
Date: 02-1994
DOI: 10.1007/BF02188581
Integrable mappings and soliton equations II
Publisher: Elsevier BV
Date: 1989
Integrable mappings and soliton equations
Publisher: Elsevier BV
Date: 05-0001
Related Organisations
Related Funding Activities
Discovery Projects - Grant ID: DP180100201
Start Date: 2018
End Date: 12-2023
Amount: $401,706.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP140100383
Start Date: 2014
End Date: 06-2020
Amount: $402,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0774473
Start Date: 2007
End Date: 12-2012
Amount: $270,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP110100077
Start Date: 2011
End Date: 12-2015
Amount: $780,000.00
Funder: Australian Research Council
View Funded Activity