Ergodic Theory and Dynamical Systems

Research Article

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

Robert Burtona1 and Jeffrey E. Steifa2

a1 Department of Mathematics, Kidder Hall, Oregon State University, Corvallis, OR 97331, USA

a2 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.

(Received August 17 1992)

(Revised April 27 1993)

Footnotes

† The research of the first author was supported in part by AFOSR grant # 91-0215 and NSF grant # DMS-9103738.