Statistical stability for diffeomorphisms with dominated splitting
SRB measures | Gibbs states | Dominated splitting
Alves, Bonatti and Viana proved that SRB measures exist for partially hyperbolic diffeomorphisms with mostly expanding center-unstable direction. The main tool used there is the existence of Gibbs cu-states. In this paper we prove many properties of such states, especially with respect to their relationship with the SRB measures. In particular, we prove that the Gibbs cu-states vary continuously with the diffeomorphism. As a consequence we obtain statistical stability for many open classes of diffeomorphisms with dominated splitting.