AIMS Mathematics (Jul 2020)

Entropy dimension of shifts of finite type on free groups

  • Jung-Chao Ban,
  • Chih-Hung Chang

DOI
https://doi.org/10.3934/math.2020329
Journal volume & issue
Vol. 5, no. 5
pp. 5121 – 5139

Abstract

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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.

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