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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 subsystems(More)
We present a method to construct equilibrium states via induction. This method can be used for some non-uniformly hyperbolic dynamical systems and for non-Hölder continuous potentials. It allows to prove the occurrence of phase transition. 1.1. Goal. We consider a dynamical system (X, f), where X is a compact metric space and f is topology mixing and local(More)
For the subshift of finite type Σ = {0, 1, 2} N we study the convergence and the selection at temperature zero of the Gibbs measure associated to a non-locally constant Hölder potential which admits exactly two maximizing ergodic measures. These measures are Dirac measures at two different fixed points and the potential is flatter at one of these two fixed(More)
We study the time of nth return of orbits to some given (union of) rect-angle(s) of a Markov partition of an Axiom A diffeomorphism. Namely, we prove the existence of a scaled generating function for these returns with respect to any Gibbs measure (associated to a Hölderian potential). As a by-product, we derive precise large deviation estimates and a(More)