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https://ah.nccu.edu.tw/handle/140.119/133715
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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: | https://doi.org/10.1063/1.5124073 |
| Appears in Collections: | [應用數學系] 期刊論文 |
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