Decay of Correlations, Quantitative Recurrence and Logarithm Law for Contracting Lorenz Attractors

摘要

In this paper we prove that a class of skew products maps with non uniformly hyperbolic base has exponential decay of correlations. We apply this to obtain a logarithm law for the hitting time associated to a contracting Lorenz attractor at all the points having a well defined local dimension, and a quantitative recurrence estimation.