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Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.
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참고문헌 (20)
참고문헌 신청
M. Boyle / 1998 / Bounded topological orbit equivalence and C-algebras / J. Math. Soc. Japan 50(2):317~329
N. Brownlowe / 2017 / Graph algebras and orbit equiva-lence / Ergodic Theory Dynam. Systems 37(2):389~417
T. Carlsen / 2019 / Flow equivalence and orbit equivalence for shifts of nite type and isomorphism of their groupoids / J. Math. Anal. Appl 469(2):1088~1110
T. M. Carlsen / 2018 / Orbit equivalence of graphs and isomorphism of graph groupoids / Math. Scand 123(2):239~248
V. Deaconu / 1995 / Groupoids associated with endomorphisms / Trans. Amer. Math. Soc 347(5):1779~1786
N. Brownlowe / 2017 / Graph algebras and orbit equiva-lence / Ergodic Theory Dynam. Systems 37(2):389~417
T. Carlsen / 2019 / Flow equivalence and orbit equivalence for shifts of nite type and isomorphism of their groupoids / J. Math. Anal. Appl 469(2):1088~1110
T. M. Carlsen / 2018 / Orbit equivalence of graphs and isomorphism of graph groupoids / Math. Scand 123(2):239~248
V. Deaconu / 1995 / Groupoids associated with endomorphisms / Trans. Amer. Math. Soc 347(5):1779~1786
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