Flow equivalence and isotopy for subshifts

Abstract

ABSTRACTWe 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 such an orbit-preserving 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.