Geometrical and measure-theoretic structures of maps with mostly expanding center

2019/04/24 by Yang, Jiagang · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.10880

Abstract

In this paper we study physical measures for \C^1+α partially hyperbolic diffeomorphisms with mostly expanding center. We show that every diffeomorphism with mostly expanding center direction exhibits a geometrical-combinatorial structure, which we call skeleton, that determines the number, basins and supports of the physical measures. Furthermore, the skeleton allows us to describe how physical measures bifurcate as the diffeomorphism changes under C¹ topology. Moreover, for each diffeomorphism with mostly expanding center, there exists a C¹ neighborhood, such that diffeomorphism among a C¹ residual subset of this neighborhood admits finitely many physical measures, whose basins have full volume. We also show that the physical measures for diffeomorphisms with mostly expanding center satisfy exponentially decay of correlation for any Hölder observes.

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• Variety of physical measures in partially hyperbolic systems with multi 1-D centers

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