Fluctuations in the time periods of a model chaotic system

Abstract

We study the fluctuations in the density of time periods of the closed orbits of a model chaotic system. The work is motivated by a similar study on integrable systems, where the existence of universalities in the fluctuation measures is established. We find that the nearest-neighbor spacing distribution exhibits linear repulsion and is well approximated by a one-parameter additive random matrix model. The spectral rigidity is more revealing and clearly shows that the fluctuations lie between those of Poisson-distributed periods and the Gaussian orthogonal ensemble of matrices. The question of universalities, however, remains open. This study should serve as a guide in settling the issue.