On flow equivalence of one-sided topological Markov shifts

TL;DR

This paper introduces new concepts of suspension and flow equivalence for one-sided topological Markov shifts, establishing their equivalence to orbit equivalence and analyzing invariance properties of associated zeta functions.

Contribution

It defines one-sided suspension and flow equivalence, proves their equivalence to orbit equivalence, and studies invariance of zeta functions under these equivalences.

Findings

One-sided flow equivalence is equivalent to continuous orbit equivalence.

The zeta function of the flow on a one-sided suspension is a dynamical zeta function.

The set of certain dynamical zeta functions is invariant under one-sided flow equivalence.

Abstract

We introduce notions of suspension and flow equivalence on one-sided topological Markov shifts, which we call one-sided suspension and one-sided flow equivalence, respectively. We prove that one-sided flow equivalence is equivalent to continuous orbit equivalence on one-sided topological Markov shifts. We also show that the zeta function of the flow on a one-sided suspension is a dynamical zeta function with some potential function and that the set of certain dynamical zeta functions is invariant under one-sided flow equivalence of topological Markov shifts.