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Annals of Mathematics, II. Series Vol. 149, No. 3, pp. 755783 (1999) 

Dimension and product structure of hyperbolic measuresLuis Barreira, Yakov Pesin and Jörg SchmelingReview from Zentralblatt MATH: The main object studied in the paper is a $C^{1+\alpha}$ diffeomorphism $T$ of a compact smooth Riemannian manifold without boundary. The authors prove that every $T$invariant hyperbolic measure possesses asymptotically ``almost'' local product structure in the sense that its density can be approximated by the product of densities on stable and unstable invariant manifolds. This property is used in the paper to prove the longstanding EckmannRuelle conjecture claiming that the pointwise dimension of every hyperbolic measure invariant under a $C^{1+\alpha}$ diffeomorphism exists almost everywhere. As a corollary this result implies that a number of important dimension type characteristics of the measure, such as the Hausdorff dimension, box and information dimensions, etc., coincide. Reviewed by Michael L.Blank Keywords: hyperbolic measure; product structure; dimension Classification (MSC2000): 37A99 28D05 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
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