Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps.

Commun. Math. Phys. 340 (2015) 901-938.

Vitor Araújo, Ian Melbourne and Paulo Varandas

Abstract

We prove that every geometric Lorenz attractor has superpolynomial decay of correlations with respect to the unique SRB measure. Moreover, we prove the Central Limit Theorem and Almost Sure Invariance Principle for the time-1 map of the flow of geometric Lorenz attractors. In particular, our results apply to the classical Lorenz attractor.

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Typos, etc: The proof of smoothness of the stable foliation presupposes that the foliation foliates. This is rectified in this paper by Araújo & Melbourne in 2017.