Research article

Entropy dimension of shifts of finite type on free groups

  • Received: 08 March 2020 Accepted: 03 June 2020 Published: 12 June 2020
  • MSC : 37A35, 37B10

  • 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.

    Citation: Jung-Chao Ban, Chih-Hung Chang. Entropy dimension of shifts of finite type on free groups[J]. AIMS Mathematics, 2020, 5(5): 5121-5139. doi: 10.3934/math.2020329

    Related Papers:

  • 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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