Almost sure rates of mixing for partially hyperbolic attractors

TL;DR

This paper develops a framework using random towers to analyze the almost sure rates of correlation decay in random partially hyperbolic attractors, providing new results applicable to various perturbed systems.

Contribution

It introduces a novel random tower approach to establish almost sure decay rates for correlation in partially hyperbolic attractors, extending to several classes of perturbed systems.

Findings

Established almost sure exponential, stretched exponential, and polynomial decay rates.

Applied the framework to small random perturbations of Axiom A and derived systems.

Demonstrated the method on solenoidal attractors with intermittency.

Abstract

We introduce random towers to study almost sure rates of correlation decay for random partially hyperbolic attractors. Using this framework, we obtain abstract results on almost sure exponential, stretched exponential and polynomial correlation decay rates. We then apply our results to small random perturbations of Axiom A attractors, small perturbations of derived from Anosov partially hyperbolic systems and to solenoidal attractors with random intermittency.