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Title: Entropy Dimension of Shifts of Finite Type on Free Groups
Authors: 班榮超
Ban, Jung-Chao
Chang, Chih-Hung
Contributors: 應數系
Keywords: topological degree;entropy dimension;free group;finitely generated group;Cayley graph;conjugacy-invariant
Date: 2020-06
Issue Date: 2021-01-25 14:25:09 (UTC+8)
Abstract: This paper considers the topological degree of G-shifts of finite type for the case where G is a finitely generated free group. Topological degree is the logarithm of entropy dimension; that is, topological degree is a characterization for zero entropy systems. Following the conjugacy-invariance of topological degree, we show that it is equivalent to solving a system of nonlinear recurrence equations. More explicitly, the topological degree of G-shift of finite type is achieved as the maximal spectral radius of a collection of matrices corresponding to the shift itself.
Relation: AIMS Mathematics, 2020, Volume 5, Issue 5, 5121-5139
Data Type: article
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