Spectral properties of the Ruelle operator for product-type potentials on shift spaces

DOI10.1112/jlms.12031zbMath1439.37025arXiv1605.07936OpenAlexW3123018275MaRDI QIDQ5357280

Manuel Stadlbauer, Manfred Denker, Leandro M. Cioletti, Artur Oscar Lopes

Publication date: 14 September 2017

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.07936

zbMATH Keywords

Ruelle operatorBernoulli equilibriumBowen's conditionclass of potentials

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodicity, mixing, rates of mixing (37A25) Classical equilibrium statistical mechanics (general) (82B05) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Symbolic dynamics (37B10) Dynamical aspects of statistical mechanics (37A60)

Related Items (11)

Symmetric Measures, Continuous Networks, and Dynamics ⋮ On information gain, Kullback-Leibler divergence, entropy production and the involution kernel ⋮ Interactions, specifications, DLR probabilities and the Ruelle operator in the one-dimensional lattice ⋮ Ruelle operator for continuous potentials and DLR-Gibbs measures ⋮ The double transpose of the Ruelle operator ⋮ On the dimension of the space of harmonic functions on transitive shift spaces ⋮ Correlation inequalities and monotonicity properties of the Ruelle operator ⋮ Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with Markovian structure ⋮ Haar systems, KMS states on von Neumann algebras and \(C^*\)-algebras on dynamically defined groupoids and noncommutative integration ⋮ The involution kernel and the dual potential for functions in the Walters' family ⋮ Product type potential on the one-dimensional lattice systems: selection of maximizing probability and a large deviation principle

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