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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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Convergence of the Ruelle operator for a function satisfying Bowen’s condition
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by Peter Walters PDF
Trans. Amer. Math. Soc. 353 (2001), 327-347 Request permission

Abstract:

We consider a positively expansive local homeomorphism $T\colon X\to X$ satisfying a weak specification property and study the Ruelle operator $\mathcal {L}_\varphi$ of a real-valued continuous function $\varphi$ satisfying a property we call Bowen’s condition. We study convergence properties of the iterates $\mathcal {L}_\varphi ^n$ and relate them to the theory of equilibrium states.
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Additional Information
  • Peter Walters
  • Affiliation: University of Warwick, Mathematics Institute, Coventry CV4 7AL, England
  • Email: pw@maths.warwick.ac.uk
  • Received by editor(s): August 9, 1999
  • Published electronically: September 13, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 327-347
  • MSC (2000): Primary 37D35; Secondary 28D20, 37A30, 37B10
  • DOI: https://doi.org/10.1090/S0002-9947-00-02656-8
  • MathSciNet review: 1783787