Statistical properties of piecewise smooth hyperbolic systems in high dimensions

N. Chernov

doi:10.3934/dcds.1999.5.425

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1999, Volume 5, Issue 2: 425-448. Doi: 10.3934/dcds.1999.5.425

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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

Received: November 1997

Revised: May 1998

Published: April 1999

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Abstract

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.

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Mathematics Subject Classification: 58F15.

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