Walters' regularity condition (Q2731041)
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scientific article; zbMATH DE number 1625457
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Walters' regularity condition |
scientific article; zbMATH DE number 1625457 |
Statements
20 January 2002
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invariant measures
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equilibrium states
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thermodynamic formalism
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Walter condition
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maximizing measures
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normal forms
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Walters' regularity condition (English)
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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)] \textit{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. NEWLINENEWLINENEWLINEBy generalizing observations due to \textit{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.
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