Quantitative statistical properties for two dimensional partially hyperbolic systems

In the last years, an extremely powerful method has been developed: the functional approach. It consists in the study of the spectral properties of the transfer operators on suitable Banach spaces. In this work we apply this approach to partially hyperbolic systems in two dimensions, establishing the germ of a general theory. To illustrate the scope of the theory, the results are used in the case of fast-slow partially hyperbolic systems, pointing out how to pursue the arguments for further progresses.