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Convergence of the Ruelle operator for a function satisfying Bowen's condition


Author: Peter Walters
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
Published electronically: September 13, 2000
MathSciNet review: 1783787
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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

DOI: https://doi.org/10.1090/S0002-9947-00-02656-8
Keywords: Transfer operator, equilibrium state, entropy
Received by editor(s): August 9, 1999
Published electronically: September 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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