On the uniqueness of Gibbs states in some dynamical systems
type: Item
instance of: scholarly article
title: On the uniqueness of Gibbs states in some dynamical systems
zbMATH Open document ID: 1196.37078
published in: Journal of Mathematical Sciences (New York)
publication date: 2010-01-19T00:00:00Z
review text: This paper is translated from Sovremennaya Matematika i Eë Prilozheniya [Contemporary Mathematics and It's Applications, Vol 61, Optimal Control, (2008)]. By applying the Grothendieck theory and Ruelle thermodynamics formalism, the authors prove that for expansive dynamical systems and interaction potentials satisfying certain analyticity conditions, the associated Gibbs states are unique. This result allows the authors to obtain an analogy between some quantities in classical thermodynamics and abstract dynamics in the spirit of the authors' previous work.
reviewed by: Xingfu Zou
Mathematics Subject Classification ID: 37E30
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 82C05
zbMATH DE Number: 5660116
zbMATH Keywords: expansive dynamical system
zbMATH Keywords: Gibbs state
zbMATH Keywords: Grothendieck theory
zbMATH Keywords: Ruelle thermodynamic formalism
zbMATH Keywords: free energy function
author: Alejandro Mesón
author: Fernando Vericat
MaRDI profile type: Publication
full work available at URL: s10958-009-9550-8
OpenAlex ID: W1984133285
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DOI: 10.1007/S10958-009-9550-8
description: scientific article; zbMATH DE number 5660116