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

@inproceedings{Michimoto2022TopologicalEF, title={Topological entropy for countable Markov shifts and Exel--Laca algebras}, author={Yuta Michimoto and Yushi Nakano and Hisayoshi Toyokawa and Keisuke Yoshida}, year={2022} }

A bstract . Weshowthatthe(Gurevich)topologicalentropyforthecountableMarkov shiftassociatedwithaninﬁnitetransitionmatrix A coincides with thenon-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.

## One Citation

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