New York Journal of Mathematics
Volume 27 (2021), 1375-1414


Kengo Matsumoto

Flow equivalence of topological Markov shifts and Ruelle algebras

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Published: September 25, 2021.
Keywords: Topological Markov shift, flow equivalence, topological conjugacy, Ruelle algerba, Cuntz--Krieger algebra.
Subject: Primary 37A55, 46L35; Secondary, 37B10, 46L55.

In this paper we study discrete flow equivalence of two-sided topological Markov shifts by using extended Ruelle algebra. We characterize flow equivalence of two-sided topological Markov shifts in terms of conjugacy of certain actions weighted by ceiling functions of two-dimensional torus on the stabilized extended Ruelle algebras for the Markov shifts.


The author would like to thank the referee for his careful reading, comments and suggestions on the first draft of the paper. This work was supported by JSPS KAKENHI Grant Number 15K04896, 19K03537.

Author information

Kengo Matsumoto:
Department of Mathematics
Joetsu University of Education
Joetsu, 943-8512, Japan