Markov Diagrams for Some Non-Markovian Systems

TL;DR

This paper explores the construction of Markov diagrams for various topological dynamical systems, including non-Markovian systems like Sturmian and substitution systems, to better understand their structures.

Contribution

It extends the application of Markov diagrams to systems without nontrivial Markovian parts, such as Sturmian and certain substitution systems.

Findings

Markov diagrams can be constructed for a broader class of systems

Some non-Markovian systems lack nontrivial Markovian components

The structure of Sturmian and substitution systems is elucidated

Abstract

Markov diagrams provide a way to understand the structures of topological dynamical systems. We examine the construction of such diagrams for subshifts, including some which do not have any nontrivial Markovian part, in particular Sturmian systems and some substitution systems.