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April  1999, 5(2): 425-448. doi: 10.3934/dcds.1999.5.425

Statistical properties of piecewise smooth hyperbolic systems in high dimensions

N. Chernov 1,

1. 

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, United States

Received  November 1997 Revised  May 1998 Published  January 1999

We study smooth hyperbolic systems with singularities and their SRB measures. Here we assume that the singularities are submanifolds, the hyperbolicity is uniform aside from the singularities, and one-sided derivatives exist on the singularities. We prove that the ergodic SRB measures exist, are finitely many, and mixing SRB measures enjoy exponential decay of correlations and a central limit theorem. These properties have been proved previously only for two-dimensional systems.
Keywords: Decay of correlations, hyperbolic dynamics., Sinai-Ruelle-Bowen measures.
Mathematics Subject Classification: 58F1.
Citation: N. Chernov. Statistical properties of piecewise smooth hyperbolic systems in high dimensions. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 425-448. doi: 10.3934/dcds.1999.5.425
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