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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 consider a class of non-conformal expanding maps on the d-dimensional torus. For an equilibrium measure of an Hölder potential, we prove an analogue of the Central Limit Theorem for the fluctuations of the logarithm of the measure of balls as the radius goes to zero. An unexpected consequence is that when the measure is not absolutely continuous , then(More)