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

## TL;DR

This paper proves exponential decay of correlations for certain skew product maps and applies these results to establish a logarithm law and recurrence estimates for contracting Lorenz attractors, enhancing understanding of their statistical properties.

## Contribution

It introduces a method to prove decay of correlations for non-uniformly hyperbolic systems and applies it to Lorenz attractors, providing new quantitative recurrence and hitting time results.

## Key findings

- Exponential decay of correlations for skew product maps.
- Logarithm law for hitting times in Lorenz attractors.
- Quantitative estimates of recurrence times.

## 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.