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Time-reversal symmetry in dynamical systems: a survey. (English) Zbl 1194.34072

Summary: 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.

MSC:

34C23 Bifurcation theory for ordinary differential equations
37Mxx Approximation methods and numerical treatment of dynamical systems
37Nxx Applications of dynamical systems
34C25 Periodic solutions to ordinary differential equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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