New results on measures of maximal entropy
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.
strongly irreducible subshift of finite type
scientific article; zbMATH DE number 755549