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

Walters, Peter

doi:10.1090/S0002-9947-00-02656-8

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