PHYSICA Time-reversal symmetry in dynamical systems: A survey

In this paper we survey the topic of time-reversal symmetry in dynamical systems. We begin with a brief discussion of the position of time-reversal symmetry in physics. After defining time-reversal symmetry as it applies to dynamical systems, we then introduce a major theme of our survey, namely the relation of time-reversible dynamical sytems to equivariant and Hamiltonian dynamical systems. We follow with a survey of the state of the art on the theory of reversible dynamical systems, including results on symmetric periodic orbits, local bifurcation theory, homoclinic orbits, and renormalization a d scaling. Some areas of physics and mathematics in which reversible dynamical systems arise are discussed. Inan appendix, we provide an extensive bibliography on the topic of time-reversal symmetry in dynamical systems