• Corpus ID: 255340717

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

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

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