2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159962We consider the notions of topological essential range and regularity for continuous cocycles over minimal $\Z$-systems introduced in \cite{GH} and discuss relations with their generic counterparts. The alternative generic definitions can be given by using the notion of generic Mackey action associated with a cocycle. We further present a description of recurrent cocycles over minimal rotations with values in discrete groups and derive several consequences.7 pagesDynamical Systems37B05, 37B20text