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

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.