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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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