Path sets in one-sided symbolic dynamics
arXiv:1207.5004 · doi:10.1016/j.aam.2013.12.005
Abstract
Path sets are spaces of one-sided infinite symbol sequences associated to pointed graphs (G_v_0), which are edge-labeled directed graphs G with a distinguished vertex v_0. Such sets arise naturally as address labels in geometric fractal constructions and in other contexts. The resulting set of symbol sequences need not be closed under the one-sided shift. this paper establishes basic properties of the structure and symbolic dynamics of path sets, and shows they are a strict generalization of one-sided sofic shifts.
16 pages, 6 figures; v2, 22pages, 6 figures; title change, adds a new Theorem 1.5, and a second Appendix, v3, 21 pages, revisions to exposition; v4 revised introduction; v5, 22 pages, changed title, revised introduction