Local product structure for Equilibrium States

Leplaideur, Renaud

doi:10.1090/S0002-9947-99-02479-4

Local product structure for Equilibrium States
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by Renaud Leplaideur

Trans. Amer. Math. Soc. 352 (2000), 1889-1912

DOI: https://doi.org/10.1090/S0002-9947-99-02479-4

Published electronically: November 17, 1999

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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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