Exponential decay of correlations for nonuniformly hyperbolic flows with a C^{1+\alpha} stable foliation, including the classical Lorenz attractor

TL;DR

This paper proves exponential decay of correlations for certain hyperbolic flows, including the classical Lorenz attractor, demonstrating robust exponential mixing under specific conditions.

Contribution

It establishes exponential decay of correlations for a class of hyperbolic flows with a $C^{1+eta}$ stable foliation, including the classical Lorenz attractor, under a nonintegrability condition.

Findings

Exponential decay of correlations for geometric Lorenz attractors.

Robust exponential mixing of the classical Lorenz attractor.

Applicability to a broad class of hyperbolic flows.

Abstract

We prove exponential decay of correlations for a class of $C^{1+\alpha}$ uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric Lorenz attractors. As a special case, we show that the classical Lorenz attractor is robustly exponentially mixing.