Dynamical correspondences for Smale spaces
Abstract
We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a correspondence is related to a matrix which intertwines the adjacency matrices of the shifts. This observation allows us to define an equivalence relation on all Smale spaces which reduces to shift equivalence for shifts of finite type. Several other notions of equivalence are introduced on both correspondences and Smale spaces; a hierarchy between these equivalences is established. Finally, we provide several methods for constructing correspondences and provide specific examples.
Cite
@article{arxiv.1505.05558,
title = {Dynamical correspondences for Smale spaces},
author = {Robin J. Deeley and D. Brady Killough and Michael F. Whittaker},
journal= {arXiv preprint arXiv:1505.05558},
year = {2016}
}
Comments
A small issue in the proof of Lemma 2.20 has been fixed and there has been a slight reorganization of the paper as a consequence