Dynamical correspondences for Smale spaces

Deeley, R., Killough, D. B. and Whittaker, M. (2016) Dynamical correspondences for Smale spaces. New York Journal of Mathematics, 22, pp. 943-988.

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Whittaker, Professor Mike
• Authors: Deeley, R., Killough, D. B., and Whittaker, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: New York Journal of Mathematics
• Publisher: College of Arts and Sciences, University at Albany
• ISSN: 1076-9803
• Copyright Holders: Copyright © 2016 The Authors
• First Published: First published in New York Journal of Mathematics 22: 943-988
• Publisher Policy: Reproduced in accordance with the publisher copyright policy