97-525 Chernov N.

STATISTICAL PROPERTIES OF PIECEWISE SMOOTH HYPERBOLIC SYSTEMS IN HIGH DIMENSIONS (96K, LATeX) Sep 28, 97

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Abstract. We study smooth hyperbolic systems with singularities and their SRB measures. Here we assume uniform hyperbolicity, aside from singularities, and the existence of one-sided derivatives on singularities. We prove that the 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 2-D systems.

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