Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz–Krieger algebras

Kengo Matsumoto

doi:10.3934/dcds.2020251

Article Contents

2020, Volume 40, Issue 10: 5897-5909. Doi: 10.3934/dcds.2020251

This issue Previous Article Extended symmetry groups of multidimensional subshifts with hierarchical structure Next Article A degenerate KAM theorem for partial differential equations with periodic boundary conditions

Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz–Krieger algebras

Kengo Matsumoto

Department of Mathematics, Joetsu University of Education, Joetsu, 943-8512, Japan

Received: October 31, 2019

Revised: April 30, 2020

Published: June 2020

This work was supported by JSPS KAKENHI Grant Numbers 15K04896, 19K03537

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Abstract

We study KMS states for gauge actions with potential functions on Cuntz–Krieger algebras whose underlying one-sided topological Markov shifts are continuously orbit equivalent. As a result, we have a certain relationship between topological entropy of continuously orbit equivalent one-sided topological Markov shifts.

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Mathematics Subject Classification: Primary: 46L55; Secondary: 46L35, 37B10.

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