Flow Equivalence of Shift Spaces

TL;DR

This paper investigates flow equivalence in shift spaces, introducing new invariants for classification and analyzing how entropy behaves under flow equivalence, revealing density of achievable entropies.

Contribution

It provides a new invariant for sofic $S$-gap shifts, completes classification of non-sofic $S$-gap shifts, and studies entropy density under flow equivalence.

Findings

New invariant for sofic $S$-gap shifts

Complete classification of non-sofic $S$-gap shifts

Entropy values are dense in positive reals under flow equivalence

Abstract

We study two problems related to flow equivalence of shift spaces. The first problem, the classification of $S$-gap shifts up to flow equivalence, is partially solved with the establishment of a new invariant for the sofic $S$-gap shifts and a complete classification of the non-sofic $S$-gap shifts. The second problem is an examination of the entropy of shift spaces under flow equivalence. For a wide array of classes of shift spaces with non-zero entropy, it is shown that the entropies achievable while maintaining flow equivalence are dense in $\mathbb R^+$.