A large-deviation approach to space-time chaos

TL;DR

This paper introduces a large-deviation approach using Lyapunov-exponents fluctuations and a Gaussian approximation to analyze high-dimensional chaos, revealing insights into interactions, constraints, and hyperbolicity.

Contribution

It presents a novel method employing a Gaussian approximation for large deviation functions to analyze chaos through Lyapunov-exponent fluctuations.

Findings

Quantifies interactions among degrees of freedom.

Unveils microscopic constraints like symplectic structure.

Checks the hyperbolicity of the dynamics.

Abstract

In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix $\bf D$ (a dynamical invariant itself) is measured and analysed in terms of its principal components. The application of this method to three (conservative, as well as dissipative) models, allows: (i) quantifying the strength of the effective interactions among the different degrees of freedom; (ii) unveiling microscopic constraints such as those associated to a symplectic structure; (iii) checking the hyperbolicity of the dynamics.