Statistical stability for diffeomorphisms with dominated splitting
Carlos H. Vasquez
SRB measures | Gibbs cu-states | statistical stability
Alves, Bonatti and Viana proved the existence of SRB measures for diffeomorphisms partially hyperbolic with mostly expanding center-unstable direction. The main tool used there is the existence of Gibbs cu-states. In this work we prove many properties of such states and with respect to its relationship with the SRB measures. In particular, we prove that the Gibbs cu-states varies continuously with the diffeomorphism. As consequence we conclude the statistical stability in many open classes of diffeomorphisms.