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Title: Entropy Dimension of Shift Spaces on Monoids
Authors: 班榮超
Ban, Jung-Chao
Chang, Chih-Hung
Huang, Nai-Zhu
Contributors: 應數系
Date: 2020-06
Issue Date: 2021-01-25 14:24:49 (UTC+8)
Abstract: We consider the entropy dimension of G-shifts of finite type for the case where G is a non-Abelian monoid. Entropy dimension tells us whether a shift space has zero topological entropy. Suppose the Cayley graph CG of G has a finite representation (that is, {CgG : g ∈ G} is a finite set up to graph isomorphism), and relations among generators of G are determined by a matrix A. We reveal an association between the characteristic polynomial of A and the finite representation of the Cayley graph. After introducing an algorithm for the computation of the entropy dimension, the set of entropy dimensions is related to a collection of matrices in which the sum of each row of every matrix is bounded by the number of leaves of the graph. Furthermore, the algorithm extends to G having finitely many free-followers.
Relation: Journal of Mathematical Physics, 61, 072702
Data Type: article
DOI 連結:
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