Topological entropy for countable Markov shifts and Exel--Laca algebras

Yuta Michimoto; Yushi Nakano; Hisayoshi Toyokawa; Keisuke Yoshida

Topological entropy for countable Markov shifts and Exel--Laca algebras

Operator Algebras 2023-01-02 v1 Dynamical Systems

Authors: Yuta Michimoto , Yushi Nakano , Hisayoshi Toyokawa , Keisuke Yoshida

Abstract

We show that the (Gurevich) topological entropy for the countable Markov shift associated with an infinite transition matrix $A$ coincides with the non-commutative topological entropy for the Exel--Laca algebra associated with $A$ , under certain conditions on $A$ . An important example satisfying the conditions is the renewal shift, which is not locally finite. We also pose interesting questions for future research on non-commutative topological entropy for non-locally finite transition matrices.

Keywords

topological entropy countable markov shift exel-laca algebra transition matrix renewal shift non-commutative entropy

Cite

@article{arxiv.2212.14607,
  title  = {Topological entropy for countable Markov shifts and Exel--Laca algebras},
  author = {Yuta Michimoto and Yushi Nakano and Hisayoshi Toyokawa and Keisuke Yoshida},
  journal= {arXiv preprint arXiv:2212.14607},
  year   = {2023}
}

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47 pages

Topological entropy for countable Markov shifts and Exel--Laca algebras

Abstract

Keywords

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