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Entropy rigidity of Anosov flows in dimension three

Published online by Cambridge University Press:  06 August 2001

PATRICK FOULON
PATRICK FOULON
Affiliation:
U.M.R. 7501 du C.N.R.S, Institut de Recherche Mathématique Avancée, 7 rue René Descartes, 67084 Strasbourg Cédex, France (e-mail: [email protected])
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Abstract

We show that for a smooth contact Anosov flow on a closed three manifold the measure of maximal entropy is in the Lebesgue class if and only if the flow is, up to finite covers, conjugate to the geodesic flow of a metric of constant negative curvature on a closed surface. This shows that the ratio between the measure theoretic entropy and the topological entropy of a contact Anosov flow is strictly smaller than one on any closed three manifold which is not a Seifert bundle.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 4 , August 2001 , pp. 1101 - 1112
Copyright
2001 Cambridge University Press

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