On the topological essential range and regularity of cocycles over compact and generic systems

Details On the topological essential range and regularity of cocycles over compact and generic systems On the topological essential range and regularity of cocycles over compact and generic systems

2008-04-29

arxiv.org/abs/0804.4570v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

We 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.

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