Exponential Decay of Correlations for Nonuniformly Hyperbolic Flows with a $${{C^{1+\alpha}}}$$ C 1 + α 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.