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

Abstract

We consider a positively expansive local homeomorphism T : X → X satisfying a weak specification property and study the Ruelle operator Lϕ of a real-valued continuous function ϕ satisfying a property we call Bowen's condition. We study convergence properties of the iterates L n ϕ and relate them to the theory of equilibrium states.