Empirical measures of partially hyperbolic diffeomorphisms

We will first talk about the limits of empirical measures of typical points assuming some weak form of hyperbolicity and we will explain some generalization of the work on u-Gibbs states by Pesin-Sinai and Bonatti-Diaz-Viana. Then we focus on some applications on the existence of SRB measures in partially hyperbolic setting with one-dimensional center. This is a joint work with S. Crovisier and D. Yang.