Analytical treatment of the chaotic behaviour of the deterministic pseudolinear map: decay of correlations and stability of periodical systems

Abstract

It was received the rate of chaotization for pseudolinear mapping. It was shown that the rate of chaotization is proportional to the dimension of the phase space and maximal Lyapunov exponent. It was shown also that the problem of the rate of chaotization is not correct and must be regularized. It was investigated also the two-dimensional dynamical system stability in the case of two and three step periodical standard maps. The stability conditions were obtained. The analytical expressions of the bounders of stability regions were written. It had been shown that the summary region of stability is expanded, when compared to the case of the one-step map, but the number of stable points decreases.