We consider a discrete dynamical system $f: M \to M$, where $M$ is a Riemannian manifold and $f$ is a diffeomorphism. We assume that the dynamical system has a Gibbs-Markov-Young structure, which consists of a reference set $\Lambda$ with a hyperbolic product structure that satisfies certain properties. The properties assumed here are the existence of a Markov partition $\Lambda_1,\dots,\Lambda_d$ of $\Lambda$, polynomial contraction on stable leaves, polynomial backwards contraction on unstable leaves, a bounded distortion property and a certain regularity of the stable foliation. We will show results establishing a control on the decay of correlations and large deviations.

Joint work with José F. Alves