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Hyperbolic measures with transverse intersections of stable and unstable manifolds

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  • Let $f$ be a diffeomorphism of a manifold preserving a hyperbolic Borel probability measure $ μ $ having transverse intersections for almost every pair of stable and unstable manifolds. A lower bound on the Hausdorff dimension of generic sets is given in terms of the Lyapunov exponents and the metric entropy. Furthermore we obtain a lower bound for the large deviation rate.
    Mathematics Subject Classification: 37A50, 37C40, 37C45, 37D25.


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