Instability statistics and mixing rates

TL;DR

This paper introduces a method using finite-time Lyapunov exponent distributions and their large deviation properties to quantitatively estimate decay rates of correlations and recurrences in weakly chaotic dynamical systems.

Contribution

It proposes a novel approach linking finite-time Lyapunov exponents to mixing rates, providing a powerful tool for analyzing systems with weak chaos.

Findings

Finite-time Lyapunov exponents reveal decay rates of correlations.

Large deviation analysis offers quantitative estimates of mixing.

Applicable to dynamical systems with weak chaotic behavior.

Abstract

We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincar\'e recurrences in the -quite delicate- case of dynamical systems with weak chaotic properties.