Conjugacy of transitive SFTs minus periodic points

TL;DR

This paper investigates whether transitive SFTs with the same entropy remain conjugate after removing periodic points, providing a negative answer and establishing a canonical correspondence between conjugacies of original and modified systems.

Contribution

It demonstrates that topological conjugacies of transitive SFTs correspond directly to those of their periodic point-removed systems, countering Hochman's question.

Findings

No, conjugacy does not necessarily hold after removing periodic points.

A canonical correspondence exists between conjugacies of original and periodic point-removed systems.

The result applies to transitive SFTs with the same entropy.

Abstract

It is a question of Hochman whether any two one-dimensional topologically mixing subshifts of finite type (SFTs) with the same entropy are topologically conjugate when their periodic points are removed. We give a negative answer, in fact we prove the stronger result that there is a canonical correspondence between topological conjugacies of transitive SFTs and topological conjugacies between the systems obtained by removing the periodic points.