A relation between Lyapunov exponents, Hausdorff dimension and entropy

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Abstract

For an Axiom A diffeomorphism of a surface with an ergodic invariant measure we prove that the entropy is the product of the positive Lyapunov exponent and the Hausdorff dimension of the set of generic points in an unstable manifold. © 1981, Cambridge University Press. All rights reserved.

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Manning, A. (1981). A relation between Lyapunov exponents, Hausdorff dimension and entropy. Ergodic Theory and Dynamical Systems, 1(4), 451–459. https://doi.org/10.1017/S0143385700001371

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