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Transactions of the American Mathematical Society

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Local product structure for Equilibrium States


Author: Renaud Leplaideur
Journal: Trans. Amer. Math. Soc. 352 (2000), 1889-1912
MSC (2000): Primary 37D20, 37D35
DOI: https://doi.org/10.1090/S0002-9947-99-02479-4
Published electronically: November 17, 1999
MathSciNet review: 1661262
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Abstract: The usual way to study the local structure of Equilibrium State of an Axiom-A diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold. A new geometrical method is given. It consists in proving that Equilibrium States for Hölder-continuous functions are related to other Equilibrium States of some special sub-systems satisfying a sort of expansiveness. Using different kinds of extensions the local product structure of Gibbs-measure is proven.


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Additional Information

Renaud Leplaideur
Affiliation: Laboratoire de Mathématique et Applications des Mathématiques, Université de Bretagne-Sud, 1, rue de la Loi, 56000 Vannes, France
Email: Renaud.Le-Plaideur@univ-ubs.fr

DOI: https://doi.org/10.1090/S0002-9947-99-02479-4
Received by editor(s): June 30, 1997
Published electronically: November 17, 1999
Article copyright: © Copyright 2000 American Mathematical Society