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Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/133715

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:	https://doi.org/10.1063/1.5124073
DOI:	10.1063/1.5124073
Appears in Collections:	[應用數學系] 期刊論文

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