Large and moderate deviations for slowly mixing dynamical systems

Abstract

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