Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry

Abstract

The structure of the differential or difference equations used to model a complex real-life system should reflect some of the underlying symmetries of the system. Characterising and exploiting this structure can lead to better prediction and explanation of the motion. For example, a well-studied structure is that found in Hamiltonian or conservative dynamical systems. In this paper, we survey our work on dynamical systems with another type of structure, namely a (generalised) time-reversal symmetry. We explain some of the dynamical consequences and structure arising from this property. We explore the question of how systems with this (generalized) time-reversal symmetry are similar to, and how they differ from, Hamiltonian dynamical systems. We pay particular attention to low-dimensional (2D and 3D) systems and use specific examples to illustrate our points.KeywordsPeriodic OrbitPhase PortraitReversible MappingHyperbolic ElementSymmetric Periodic OrbitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.