Local product structure for Equilibrium States

Renaud Leplaideur
1999 Transactions of the American Mathematical Society  
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.
doi:10.1090/s0002-9947-99-02479-4 fatcat:t7euoob3zvba7g3r2phgfvo57m