Abstract
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.
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