|Título||On the Aubry-Mather theory for symbolic dynamics
Lopes, Artur Oscar
|Abstract||We 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 Holder potentials also in the holonomic setting. We analyze then connections between calibrated sub-actions and the Ma˜n´e 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.
|Contido em||Ergodic theory and dynamical systems. Cambrige. Vol. 28, no. 4 (June 2008), p. 791-815.
Sistemas dinamicos : Ergodicidade : Topologia
|Tipo||Artigo de periódico
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