Symmetry Decomposition of Chaotic Dynamics

TL;DR

This paper develops a formalism for symmetry decomposition in chaotic dynamical systems, demonstrating how discrete symmetries simplify analysis and improve spectral calculations, with applications to the N-disk pinball model.

Contribution

It introduces a general formalism for symmetry decomposition in chaotic flows and applies it to the N-disk pinball model, enhancing spectral analysis methods.

Findings

Symmetry factorizations improve convergence of cycle expansions.

Application to N-disk model illustrates practical benefits.

Reduces computational effort in spectral analysis.

Abstract

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.