Classification of eventually periodic subshifts

TL;DR

This paper classifies eventually periodic subshifts based on conjugacy and flow equivalence, revealing unique conjugacy classes among skew Sturmian subshifts and their universal flow equivalence.

Contribution

It provides a complete classification of eventually periodic subshifts and establishes conjugacy and flow equivalence relations among skew Sturmian subshifts.

Findings

Each skew Sturmian subshift is conjugate to exactly one other skew Sturmian subshift.

All skew Sturmian subshifts are flow equivalent.

The classification clarifies the structure of eventually periodic subshifts.

Abstract

We provide a classification of eventually periodic subshifts up to conjugacy and flow equivalence. We use our results to prove that each skew Sturmian subshift is conjugate to exactly one other skew Sturmian subshift and that all skew Sturmian subshifts are flow equivalent to one another.