Large and Moderate Deviations for Slowly Mixing Dynamical Systems

We obtain results on large deviations for a large class of nonuniformly hyperbolic dynamical systems with polynomial decay of correlations 1/nβ, β > 0. This includes systems modelled by Young towers with polynomial tails, extending recent work of M. Nicol and the author which assumed β > 1. As a byproduct of the proof, we obtain slightly stronger results even when β > 1. The results are sharp in the sense that there exist examples (such as PomeauManneville intermittency maps) for which the obtained rates are best possible. In addition, we obtain results on moderate deviations.