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Local product structure for equilibrium states. (English) Zbl 0995.37017
Summary: 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.

MSC:
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
28D20 Entropy and other invariants
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