On factor maps that send Markov measures to Gibbs measures
type: Item
instance of: scholarly article
title: On factor maps that send Markov measures to Gibbs measures
zbMATH Open document ID: 1211.82026
author: Jisang Yoo
published in: Journal of Statistical Physics
publication date: 2011-01-07T00:00:00Z
review text: Let \(X\) and \(Y\) be mixing shifts on finite type. Let \(\pi\) be a factor map from \(X\) to \(Y\) that is fiber-mixing, i.e., given \(x, \tilde{x} \in X\) with \(\pi(x)=\pi(\tilde{x})=y \in Y\), there is \(z\in \pi^{-1}(y) \) that is left asymptotic to \(x\) and right asymptotic to \(\tilde{x}.\) The author shows that a fiber-mixing condition is sufficient for the factor map to send all Markov measures to a Cibbs measures. The fiber-mixing condition turned out to be conjugacy-invariant and time -symmetric. It is presented an example showing that this generalization is nonempty.
reviewed by: Nasir N. Ganikhodjaev
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 5833854
zbMATH Keywords: Markov measure
zbMATH Keywords: sofic measure
zbMATH Keywords: Gibbs measure
zbMATH Keywords: hidden Markov chain
zbMATH Keywords: fiber-mixing
zbMATH Keywords: thermodynamic formalism
MaRDI profile type: Publication
full work available at URL: s10955-010-0084-8
OpenAlex ID: W1971500046
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DOI: 10.1007/S10955-010-0084-8
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description: scientific article; zbMATH DE number 5833854