On flow-equivalence of R-graph shifts

TL;DR

This paper investigates flow equivalence in symbolic dynamics, demonstrating invariance of Property (A) and semigroup structures, and establishing conditions under which R-graph shifts are flow equivalent to isomorphic R-graphs.

Contribution

It proves that Property (A) and associated semigroups are invariants under flow equivalence, and links flow equivalence of R-graph shifts to R-graph isomorphism.

Findings

Property (A) is invariant under flow equivalence.

Semigroup structures associated with subshifts are invariants.

Flow equivalence of R-graph shifts implies R-graph isomorphism for certain classes.

Abstract

We show that Property $(A)$ of subshifts and the semigroup, that is associated to subshifts with Property (A), are invariants of flow equivalence. We show for certain $\mathcal R$-graphs that their isomorphism is implied by the flow equivalence of their $\mathcal R$-graph shifts.