Conjugacy of local homeomorphisms via groupoids and C*-algebras

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We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include self-covering maps, one-sided shifts of finite type and, more generally, the boundary-path spaces of directed and topological graphs. We characterize the topological conjugacy of these systems in terms of isomorphisms of their associated groupoids and C*-algebras. This significantly generalizes recent work of Matsumoto and of the second- and third-named authors.

OriginalsprogEngelsk
TidsskriftErgodic Theory and Dynamical Systems
Vol/bind43
Udgave nummer8
Sider (fra-til)2516–2537
Antal sider22
ISSN0143-3857
DOI
StatusUdgivet - 2023

ID: 343215111