2020/09/23 by Shaobo Gan, Gan, Shaobo, Fan Yang +5
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Chaos control and synchronization
paper · pdf · doi:10.48550/arxiv.2009.11089
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 C1 diffeomorphisms \fn\ must be a Gibbs F-state for the limiting map f. As a consequence, we establish the statistical stability for the C1 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.