Carlangelo Liverani

Quantitive statistical properties for partially hyperbolic system

In the last years it has been developed a theory to study the ergodicity of partially hyperbolic systems, however not much is known about stronger statistical properties. Unfortunately, for many applications precise estimates on the decay of correlations and limit theorems with explicit errors are needed. It is then of paramount importance to develop a theory capable of addressing such questions. I will discuss some attempts in this direction focusing on a simple but far reaching example.