Necessary and sufficient conditions for a dynamical system to be topologically conjugate to a given substitution minimal system

TL;DR

This paper establishes precise conditions under which a dynamical system is topologically conjugate to a specific substitution minimal system, generalizing previous results for Morse and Toeplitz substitutions.

Contribution

It provides necessary and sufficient criteria for topological conjugacy to substitution minimal systems, extending prior work to a broader class of systems.

Findings

Derived conditions for topological conjugacy

Extended results to general substitution minimal systems

Unified framework for Morse and Toeplitz cases

Abstract

We find necessary and sufficient conditions for a dynamical system to be topologically conjugate to any given substitution minimal system, thus extending the results in [CKL] for the Morse and Toeplitz substitutions.