Maximal Large Deviations and Slow Recurrences in Weakly Chaotic Systems

TL;DR

This paper establishes a maximal large deviation principle for weakly chaotic dynamical systems with slow mixing, providing new insights into their statistical behavior, especially in billiard models.

Contribution

It introduces a maximal large deviation principle applicable to systems with slow polynomial mixing, extending understanding of their probabilistic properties.

Findings

Maximal large deviation principle proven for slow mixing systems

Applications demonstrated in billiard systems

Enhanced understanding of statistical fluctuations in weakly chaotic dynamics

Abstract

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.