Conjugacy of local homeomorphisms via groupoids and C*-algebras
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Conjugacy of local homeomorphisms via groupoids and C*-algebras. / Armstrong, Becky; Brix, Kevin Aguyar; Carlsen, Toke Meier; Eilers, Søren.
In: Ergodic Theory and Dynamical Systems, Vol. 43, No. 8, 2023, p. 2516–2537.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Conjugacy of local homeomorphisms via groupoids and C*-algebras
AU - Armstrong, Becky
AU - Brix, Kevin Aguyar
AU - Carlsen, Toke Meier
AU - Eilers, Søren
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - conjugacy
KW - local homeomorphism
KW - Deaconu-Renault system
KW - groupoid
KW - C-algebra
KW - TOPOLOGICAL ORBIT EQUIVALENCE
KW - GRAPH ALGEBRAS
KW - MARKOV SHIFTS
KW - FLOW EQUIVALENCE
KW - DIMENSION
KW - SUBSHIFTS
U2 - 10.1017/etds.2022.50
DO - 10.1017/etds.2022.50
M3 - Journal article
VL - 43
SP - 2516
EP - 2537
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 8
ER -
ID: 343215111