Markov-Dyck shifts, neutral periodic points and topological conjugacy

TL;DR

This paper investigates the relationship between the topological conjugacy of Markov-Dyck shifts and the isomorphism of their underlying graphs, focusing on neutral periodic points and specific structural conditions.

Contribution

It establishes that, under certain conditions, topological conjugacy of Markov-Dyck shifts implies the isomorphism of the associated graphs, advancing understanding of their structural classification.

Findings

Topological conjugacy implies graph isomorphism under certain conditions

Neutral periodic points are key to distinguishing graph structures

Structural hypotheses are crucial for the main conjugacy-isomorphism result

Abstract

We study the neutral periodic points of the Markov-Dyck shifts of finite strongly connected directed graphs. Under certain hypothesis on the structure of the graphs we show, that the topological conjugacy of their Markov-Dyck shifts implies the isomorphism of the graphs.