, Volume 223, Issue 1, pp 125-141

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

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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.

Received: 31 May 2000 / Accepted: 1 June 2001