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The entropy of C2 surface diffeomorphisms in terms of Hausdorff dimension and a Lyapunov exponent

Published online by Cambridge University Press:  19 September 2008

Leonardo Mendoza
Leonardo Mendoza
Affiliation:
Escuela de Ciencias, U.C.O.L.A., Apdo. 400 Barquisimeto, Venezuela
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Abstract

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In this paper we prove that if the entropy of an ergodic measure preserved by a C2 surface diffeomorphism is positive then it is equal to the product of the Hausdorff dimension of the quotient measure defined by the family of stable manifolds and the positive Lyapunov exponent.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 273 - 283
Copyright
Copyright © Cambridge University Press 1985

References

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