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A relation between Lyapunov exponents, Hausdorff dimension and entropy

Published online by Cambridge University Press:  19 September 2008

Anthony Manning
Anthony Manning
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 451 - 459
Copyright
Copyright © Cambridge University Press 1981

References

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