ORIENTATION OF PIECEWISE POWERS OF A MINIMAL HOMEOMORPHISM

Abstract We show that, given a compact minimal system $(X,g)$ and an element h of the topological full group $\tau [g]$ g , infinite orbits admit locally constant orientation with respect to . use this obtain clopen partition $(X,G)$ into periodic parts, where G is any virtually polycyclic subgroup also give refinement index map describe role in submonoid generated by induced transformations Finally, we consider problem, homeomorphism Cantor space X determining whether or not there exists such that $h \in \tau