Statistical properties of dynamical chaos.

We present a survey of the results obtained by the authors on statistical description of dynamical chaos and the effect 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 different types of attractors. We explore peculiarities of autocorrelation decay and power spectrum shape, their interconnection with Lyapunov exponents, instantaneous phase diffusion and the intensity of external noise. Numeric results are compared with experimental data.