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Dynamical correspondences for Smale spaces Public Deposited

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https://scholar.colorado.edu/concern/articles/8c97kq91n
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.
Creator
Date Issued
  • 2016-01-01
Academic Affiliation
Journal Title
Journal Volume
  • 22
File Extent
  • 943-988
Subject
Last Modified
  • 2019-12-05
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ISSN
  • 1076-9803
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