標題: Entropy dimension of shift spaces on monoids
作者: Ban, Jung-Chao
Chang, Chih-Hung
Huang, Nai-Zhu
應用數學系
Department of Applied Mathematics
公開日期: 1-七月-2020
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 C-G of G has a finite representation (that is, {C-gG : g is an element of 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.
URI: http://dx.doi.org/10.1063/1.5124073
http://hdl.handle.net/11536/154896
ISSN: 0022-2488
DOI: 10.1063/1.5124073
期刊: JOURNAL OF MATHEMATICAL PHYSICS
Volume: 61
Issue: 7
起始頁: 0
結束頁: 0
顯示於類別:期刊論文