Variational principles for topological pressure in the case of a Markov chain with a countable number of states
type: Item
instance of: scholarly article
title: Variational principles for topological pressure in the case of a Markov chain with a countable number of states
zbMATH Open document ID: 0632.60070
DOI: 10.1007/BF01158352
author: A. S. Zargaryan
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: Let \(f: X\to X\) be a continuous mapping of a compact metric space X. For a continuous \(\phi\) : \(X\to R\), one can define by \(P(X,f,\phi)\leq +\infty\) the topological pressure. This becomes the topological entropy h(X,f), when \(\phi\equiv 0\), for the same mapping f. For a set M(X,f) of invariant probabilistic measures, the topological pressure satisfies the variational principle: \[ P(X,f,\phi)=\sup_{\mu \in M(X,f)}[h_{\mu}(X,f)+\int_{X}\phi d\mu]. \] The author shows that the variational principle remains true for every uniformly continuous and bounded function \(\phi\), for a Markov chain with a countable number of states.
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 4028556
zbMATH Keywords: topological pressure
zbMATH Keywords: topological entropy
zbMATH Keywords: invariant probabilistic measures
zbMATH Keywords: variational principle
MaRDI profile type: Publication
cites work: Q4746556
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description: scientific article; zbMATH DE number 4028556