Fast-slow partially hyperbolic systems: beyond averaging. Part I (Limit Theorems)

Jacopo De Simoi, Carlangelo Liverani

Published 2014-08-23Version 1

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and conclude with a completely new result (a local limit theorem) on the distribution of the process determined by the fluctuations around the average. The method of proof is based on a mixture of standard pairs and Transfer Operators that we expect to be applicable in a much wider generality.