Flow equivalence and isotopy for subshifts
Abstract
We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map is not always an isotopy, but that this always is the case for suspension flows of irreducible shifts of finite type. We also provide a version of the fundamental discretization result of Parry and Sullivan which does not require that the flow maps are either injective or surjective. Our work is motivated by applications in the classification theory of sofic shift spaces, but has been formulated to supply a solid and accessible foundation for other purposes.
Cite
@article{arxiv.1511.03478,
title = {Flow equivalence and isotopy for subshifts},
author = {Mike Boyle and Toke Meier Carlsen and Søren Eilers},
journal= {arXiv preprint arXiv:1511.03478},
year = {2017}
}
Comments
25 pages. There are various small changes, and also a correction to a misstatement of Theorem 3.1(b) (Theorem 3.3(b) in version 1 and 2). The numbering of theorems, definitions, etc. have been changed such that it agrees with the published version