Rapid Mixing for the Lorenz Attractor and Statistical Limit Laws for Their Time-1 Maps

We prove that every geometric Lorenz attractor satisfying a strong dissipativity condition has superpolynomial decay of correlations with respect to the unique Sinai–Ruelle–Bowen measure. Moreover, we prove the central limit theorem and almost sure invariance principle for the time-1 map of the flow of such attractors. In particular, our results apply to the classical Lorenz attractor.