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arXiv · 2212.14607

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

Yuta Michimoto·Yushi Nakano·Hisayoshi Toyokawa·Keisuke Yoshida
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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.

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Yuta Michimoto, Yushi Nakano, Hisayoshi Toyokawa, Keisuke Yoshida. 2022-12-30. Topological entropy for countable Markov shifts and Exel--Laca algebras. https://arxiv.org/abs/2212.14607

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