| Résume||In the last years, an extremely powerful method has been developed to investigate the statistical properties of a dynamical system: the functional approach. It consists of the study of the spectral properties of the transfer operator on suitable Banach spaces. In this talk we will discuss how to further such a point of view to a class of two dimensional partially hyperbolic systems, not necessarily skew products, to prove existence of finitely many physical measures with smooth densities and decay of correlations. To illustrate the scopes of the theory, we will discuss how to apply the results, from a quantitative point of view, to the case of fast-slow partially hyperbolic systems.
This is a joint work with Carlangelo Liverani.|