The Analyticity of a Generalized Ruelle's Operator

Abstract

In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle operator proposed in [BCLMS] and the Perron Frobenius operator defined in [Bowen]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle operator and present some examples.

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Cited by in corpus (4)

• Spectral Properties of the Ruelle Operator on the Walters Class over Compact Spaces
• Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with markovian structure
• Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with markovian structure
• Entropy, Pressure and Duality for Gibbs plans in Ergodic Transport