Symmetry decomposition of chaotic dynamics

Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations in turn reduce the labor and improve the convergence of cycle expansions for classical and quantum spectra associated with the flow. In this paper the general formalism is developed, with the N-disk pinball model used as a concrete example and a series of physically interesting cases worked out in detail. 1 permanent address 1 Introduction The periodic orbit theory of classical chaotic dynamical systems has a long and distinguished history; initiated by Poincare1, and developed as a mathematical theory of hyperbolic dynamical systems by Smale, Sinai, Bowen, Ruelle and others2, 3, 4, 5, it has in recent years been applied to many systems of physical interest6, 7, 8, 9. The periodic orbit theory of quantum mechanical systems largely parallels this development; originating in the wor...