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.
|Journal||Ergodic Theory and Dynamical Systems|
|Number of pages||22|
|Publication status||Published - 2023|
- conjugacy, local homeomorphism, Deaconu-Renault system, groupoid, C*-algebra, TOPOLOGICAL ORBIT EQUIVALENCE, GRAPH ALGEBRAS, MARKOV SHIFTS, FLOW EQUIVALENCE, DIMENSION, SUBSHIFTS