Abstract
The usual way to study the local structure of Equilibrium State of an AxiomA 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 Holder-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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