New results on measures of maximal entropy |
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Authors: | Robert Burton Jeffrey E. Steif |
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Affiliation: | (1) Department of Mathematics, Kidder Hall Oregon State University, 97331 Corvallis, OR, USA;(2) Department of Mathematics, Chalmers University of Technology, S-412 96 Gothenburg, Sweden |
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Abstract: | It has recently been demonstrated that there are strongly irreducible subshifts of finite type with more than one measure of maximal entropy. Here we obtain a number of results concerning the uniqueness of the measure of maximal entropy. In addition, we construct for anyd≥2 andk a strongly irreducible subshift of finite type ind dimensions with exactlyk ergodic (extremal) measures of maximal entropy. Ford≥3, we construct a strongly irreducible subshift of finite type ind dimensions with a continuum of ergodic measures of maximal entropy. Research supported in part by AFOSR grant # 91-0215 and NSF grant # DMS-9103738. Research supported by the Swedish National Science Foundation. |
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