Walters’ regularity condition. (La condition de Walters.) (French) Zbl 0988.37036
In the study of invariant measures and equilibrium states for some mappings which expand distances [Trans. Am. Math. Soc. 236, 127-153 (1978; Zbl 0375.28009)] P. Walters introduced a regularity condition for the needs of the thermodynamic formalism. In particular that refers to the topological conjugacy of dynamical systems and links with Bernoulli shifts.
By generalizing observations due to R. Mañé [Nonlinearity 9, 273-310 (1996; Zbl 0886.58037)] on minimizing measures of Lagrangian systems to the hyperbolic case, the Walter condition is shown to be necessary in the study of maximizing measures, and in the search of normal forms modulo coboundaries of continuous functions.
By generalizing observations due to R. Mañé [Nonlinearity 9, 273-310 (1996; Zbl 0886.58037)] on minimizing measures of Lagrangian systems to the hyperbolic case, the Walter condition is shown to be necessary in the study of maximizing measures, and in the search of normal forms modulo coboundaries of continuous functions.
Reviewer: Piotr Garbaczewski (Zielona Gora)
MSC:
37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
37A60 | Dynamical aspects of statistical mechanics |
Keywords:
invariant measures; equilibrium states; thermodynamic formalism; Walter condition; maximizing measures; normal formsReferences:
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