Estimates of constants in the limit theorems for chaotic dynamical systems

Abstract

In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc) of the asymptotic laws and of convergence rates were studied. However, for basically all applications, e.g., for computer simulations, development of algorithms to study chaotic dynamical systems numerically, as well as for design and analysis of real (e.g., in physics) experiments, the exact values (or at least estimates) of constants (parameters) of the functions, which appear in the asymptotic laws and rates of convergence, are of primary interest. In this paper we provide such estimates of constants (parameters) in the central limit theorem, large deviations principle, law of large numbers and the rate of correlations decay for strongly chaotic dynamical systems.