Spectrum of the Frobenius-Perron operator for systems with stochastic perturbation

Abstract

We analyze the problem of evolution in a system with stochastic perturbation and point out that analytic properties of the noise present in the system might determine spectral properties of the evolution operator (Frobenius-Perron operator). We also propose a method for approximation of the spectrum and eigenvectors of the FP-operator by applying a suitable noise. Moreover we demonstrate that the eigenvalues of the FP-operator located outside the essential spectrum are robust not only against local perturbation but also against the non local perturbation and that these stable eigenvalues have a direct physical meaning: they determine the rate of the exponential decay of correlation in the system.