Estimates of constants in the limit theorems for chaotic dynamical systems

TL;DR

This paper provides estimates of key constants in limit theorems for strongly chaotic dynamical systems, which are crucial for applications like simulations and experimental analysis.

Contribution

It offers the first systematic estimates of constants in asymptotic laws for chaotic systems, enhancing practical understanding and application.

Findings

Estimated constants in the central limit theorem for chaotic systems

Provided bounds for large deviations and correlation decay rates

Improved accuracy of probabilistic predictions in chaotic dynamics

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.