On the Aubry–Mather theory for symbolic dynamics

Author:

GARIBALDI E.,LOPES A. O.

Abstract

AbstractWe propose a new model of ergodic optimization for expanding dynamical systems: the holonomic setting. In fact, we introduce an extension of the standard model used in this theory. The formulation we consider here is quite natural if one wants a meaning for possible variations of a real trajectory under the forward shift. In other contexts (for twist maps, for instance), this property appears in a crucial way. A version of the Aubry–Mather theory for symbolic dynamics is introduced. We are mainly interested here in problems related to the properties of maximizing probabilities for the two-sided shift. Under the transitive hypothesis, we show the existence of sub-actions for Hölder potentials also in the holonomic setting. We analyze then connections between calibrated sub-actions and the Mañé potential. A representation formula for calibrated sub-actions is presented, which drives us naturally to a classification theorem for these sub-actions. We also investigate properties of the support of maximizing probabilities.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference24 articles.

1. Generic properties and problems of minimizing measures of Lagrangian systems

2. Mather measures and the Bowen–Series transformation

3. Zeta functions and the periodic orbit structure of hyperbolic dynamics;Parry;Astérisque,1990

4. [22] Oliveira E. R. . Propriedades genéricas de lagrangianos e problemas variacionais holonômicos em sistemas de funções iteradas. PhD Thesis (Preliminary Version), Universidade Federal do Rio Grande do Sul, 2007.

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