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

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.

30 pages, 3 figures. Final accepted version to appear in Communications in Math Phys

References in corpus (1)

• Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

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