Full Groups and Orbit Equivalence in Cantor Dynamics
نویسنده
چکیده
In this note we consider dynamical systems (X, G) on a Cantor set X satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems (X1, G1) and (X2, G2) are orbit equivalent if and only if their full groups are isomorphic as abstract groups. This result is a topological version of the well-known Dye’s theorem established originally for ergodic measure-preserving actions.
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