A characterization of the entropies of multidimensional shifts of finite type

• 成果类型: Article
• 署名作者: Hochman, Michael; Meyerovitch, Tom
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 2011-2038
• 关键词: topological-entropy; subshifts; AUTOMORPHISMS; tilings

摘要

We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number h >= 0 is the entropy of such an SFT if and only if it is right recursively enumerable, i.e. there is a computable sequence of rational numbers converging to h from above. The same characterization holds for the entropies of sofic shifts. On the other hand, the entropy of strongly irreducible SFTs is computable.