Statistical properties of dynamical chaos

(Communicated by Stefano Boccaletti) Abstract. This study presents a survey of the results obtained by the au-thors on statistical description of dynamical chaos and the eect of noise on dynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaotic attractors and discuss methods of diagnosing the type of an attractor. We consider regularities of the relaxation to an invariant probability measure for dierent types of attractors. We explore peculiarities of autocorrelation de-cay and of power spectrum shape and their interconnection with Lyapunov exponents, instantaneous phase diusion and the intensity of external noise. Numeric results are compared with experimental data.