Slow Rates of Mixing for Dynamical Systems with Hyperbolic Structures

Abstract

We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable return time. We show that the decay of correlations of the SRB measure associated to that hyperbolic structure is related to the tail of the recurrence times. We also give sufficient conditions for the validity of the Central Limit Theorem. This extends previous results by Young in (Ann. Math. 147: 585–650, 1998; Israel J. Math. 110: 153–188, 1999).