New results on measures of maximal entropy
type: Item
instance of: scholarly article
title: New results on measures of maximal entropy
zbMATH Open document ID: 0826.28009
DOI: 10.1007/BF02808205
author: Jeffrey E. Steif
author: Robert Burton
published in: Israel Journal of Mathematics
publication date: 1995-11-19T00:00:00Z
review text: This paper is concerned with the issue of the number of measures of maximal entropy which can be supported by strongly irreducible subshift of finite type. It is known that the number need not be unique; here the authors demonstrate situations where they can specify exactly how many such measures exist. See the paper for the definitions of subshift of finite type, strongly irreducible, and entropy. It is well-known that there is always at least one measure where the entropy maximizes. The authors establish that for any \(k\geq 1\) and symbol space of \(d\geq 2\) elements, there exists a strongly irreducible subshift of finite type in \(d\) dimensions which has exactly \(k\) ergodic measures of maximal entropy. Furthermore, for \(d\geq 3\), there exists a strongly irreducible subshift of finite type in \(d\) dimensions which has a continuum of ergodic measures of maximal entropy. The authors then establish some delicate results on the number of measures of maximal entropy in particular classes of examples.
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 755549
zbMATH Keywords: measures of maximal entropy
zbMATH Keywords: strongly irreducible subshift of finite type
zbMATH Keywords: ergodic measures
reviewed by: Michael Sears
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02808205
OpenAlex ID: W2032586871
description: scientific article; zbMATH DE number 755549