Decay of correlations for some non-uniformly hyperbolic attractors

Abstract

We study the decay of correlations for certain dynamical systems with non-uniformly hyperbolic attractors, which natural invariant measure is the Sinai-Ruelle-Bowen (SRB) measure. The system $ g $ that we consider is produced by applying the slow-down procedure to a uniformly hyperbolic diffeomorphism $ f $ with an attractor. Under certain assumptions on the map $ f $ and the slow-down neighborhood, we show that the map $ g $ admits polynomial upper and lower bounds on correlations with respect to its SRB measure and the class of Hölder continuous observables. Our results apply to the Smale-Williams solenoid, as well as its sufficiently small perturbations.