Coded equivalence of one-sided topological Markov shifts

TL;DR

This paper introduces a new concept called coded equivalence for one-sided topological Markov shifts, showing it implies continuous orbit equivalence and is inspired by coding theory.

Contribution

The paper defines coded equivalence for one-sided topological Markov shifts and establishes its relationship with existing notions like topological conjugacy and orbit equivalence.

Findings

Coded equivalence implies continuous orbit equivalence.

One-sided topological conjugacy implies coded equivalence.

The notion is inspired by coding theory.

Abstract

We introduce a notion of coded equivalence in one-sided topological Markov shifts. The notion is inspired by coding theory. One-sided topological conjugacy implies coded equivalence. We will show that coded equivalence implies continuous orbit equivalence of one-sided topological Markov shifts.