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題名: | Entropy Dimension of Shift Spaces on Monoids | 作者: | 班榮超 Ban, Jung-Chao Chang, Chih-Hung Huang, Nai-Zhu |
貢獻者: | 應數系 | 日期: | 六月-2020 | 上傳時間: | 25-一月-2021 | 摘要: | 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. | 關聯: | Journal of Mathematical Physics, 61, 072702 | 資料類型: | article | DOI: | https://doi.org/10.1063/1.5124073 |
Appears in Collections: | 期刊論文 |
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