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

We investigate dynamical systems with stochastic perturbation and study to what extend analytical properties of the noise present influence the spectr um of the associated Frobenius-Perron operator. We suggest to distinguish a "physical" part of the spectrum of the deterministic system, as this robus t with respect to the perturbation. For exemplary system studied such eigen values of the FP-operator are located outside the essential spectrum and ha ve direct physical meaning: they determine the rate of the exponential deca y of correlations in the system. (C) 2001 Elsevier Science B.V. All rights reserved.