Decay of correlations, quantitative recurrence and logarithm law for contracting Lorenz attractors

Abstract

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.

23 pages, 3 figures

References in corpus (1)

• Lorenz like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence

Cited by in corpus (2)

• On the statistical stability of families of attracting sets and the contracting Lorenz attractor
• Noise induced order for skew-products over a non-uniformly expanding base