Determination of correlation spectra in chaotic systems

Abstract

We propose a new method for evaluating the decay rates of time correlations in chaotic dynamical systems, based on averaging over periodic orbits. We use a cycle expansion of a Fredholm determinant which is in practice superior to the corresponding expansion for the Ruelle ζ function. The method is tested in one-dimensional expanding maps with the resulting decay rates compared to those obtained in two other independent ways: By a perturbative calculation of the spectrum of the transfer operator and by direct numerical computations of time correlations. Moreover, we show that in general the decay rates are not simply related to generalized Lyapunov exponents.