Statistical properties of physical-like measures*

In this paper we consider the semi-continuity of the physical-like measures for diffeomorphisms with dominated splittings. We prove that any weak-* limit of physical-like measures along a sequence of C-1 diffeomorphisms {f(n)} must be a Gibbs F-state for the limiting map f. As a consequence, we establish the statistical stability for the C-1 perturbation of the time-one map of three-dimensional Lorenz attractors, and the continuity of the physical measure for the diffeomorphisms constructed by Bonatti and Viana.

Automated summary

In this paper, the semi-continuity of physical-like measures for diffeomorphisms with dominated splittings is considered, and it is proven that the weak-* limit of physical-like measures along a sequence of C-1 diffeomorphisms must be a Gibbs F-state for the limiting map f, leading to the establishment of statistical stability for perturbations of Lorenz attractors and continuity of physical measures for diffeomorphisms constructed by Bonatti and Viana.