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Non-uniqueness of measures of maximal entropy for subshifts of finite type

Published online by Cambridge University Press:  19 September 2008

Robert Burton
Affiliation:
Department of Mathematics, Kidder Hall, Oregon State University, Corvallis, OR 97331, USA
Jeffrey E. Steif
Affiliation:
Department of Mathematics, Chalmers University of Technology, S — 412 96 Gothenburg, Sweden

Abstract

It is known that in one dimension an irreducible subshift of finite type has a unique measure of maximal entropy, the so-called Parry measure. Here we give a counterexample to this in higher dimensions. For this example, we also describe the geometric structure of the measures of maximal entropy and show that there are exactly two extremal measures.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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