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

## TL;DR

This paper investigates the relationship between continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz--Krieger algebras, revealing connections with topological entropy.

## Contribution

It establishes a link between continuous orbit equivalence and KMS states, and explores how topological entropy behaves under this equivalence.

## Key findings

- KMS states are studied for gauge actions with potential functions.
- A relationship between topological entropy and orbit equivalence is identified.
- The work enhances understanding of the structure of Cuntz--Krieger algebras in relation to topological dynamics.

## Abstract

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