Jeroen S.W. Lamb & John A.G. Roberts:

Time-reversal symmetry in dynamical systems: a survey

abstract:

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 and scaling. Some areas of physics and mathematics in which
reversible dynamical systems arise are discussed. In an appendix, we provide
an extensive bibliography on the topic of time-reversal symmetry
in dynamical systems.