Invariant measures and equilibrium states for some mappings which expand distances
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- by Peter Walters PDF
- Trans. Amer. Math. Soc. 236 (1978), 121-153 Request permission
Abstract:
For a certain collection of transformations T we define a Perron-Frobenius operator and prove a convergence theorem for the powers of the operator along the lines of the theorem D. Ruelle proved in his investigation of the equilibrium states of one-dimensional lattice systems. We use the convergence theorem to study the existence and ergodic properties of equilibrium states for T and also to study the problem of invariant measures for T. Examples of the transformations T considered are expanding maps, transformations arising from f-expansions and shift systems.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 236 (1978), 121-153
- MSC: Primary 28A65; Secondary 58F15
- DOI: https://doi.org/10.1090/S0002-9947-1978-0466493-1
- MathSciNet review: 0466493