Communications in Mathematical Physics

, Volume 223, Issue 1, pp 125–141 | Cite as

On Ruelle–Perron–Frobenius Operators.¶I. Ruelle Theorem

  • Aihua Fan
  • Yunping Jiang


We study Ruelle–Perron–Frobenius operators for locally expanding and mixing dynamical systems on general compact metric spaces associated with potentials satisfying the Dini condition. In this paper, we give a proof of the Ruelle Theorem on Gibbs measures. It is the first part of our research on the subject. The rate of convergence of powers of the operator will be presented in a forthcoming paper.


Dynamical System Gibbs Measure Forthcoming Paper Dini Condition Frobenius Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Aihua Fan
    • 1
  • Yunping Jiang
    • 2
  1. 1.Département de Mathématiques et Informatique, Université de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens Cedex 1, France. E-mail: ai-huafan@u-picardie.frFR
  2. 2.Department of Mathematics, Queens College of CUNY, Flushing, NY 11367, USA and Department of Mathematics, CUNY Graduate School, 635 Fifth Avenue, New York, NY 10016, USA.¶E-mail: yunqc@jiang.math.qc.eduUS

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