Reconstruction of orbits of Cantor systems from full groups
Reconstruction of orbits of Cantor systems from full groups
In this note, we show that the topological structure of orbits of a Cantor dynamical system, satisfying some mild technical conditions, is completely determined by its full group; namely, we prove that two Cantor systems (X1, G1) and (X2, G2) are orbit equivalent if and only if their full groups …