Some applications of groups of essential values of cocycles in topological dynamics - Mentzen, Mieczysław K. (Topological Methods in Nonlinear Analysis, 2004)
A class of examples showing that a measure-theoreticalcharacterization of regular cocycles in terms of essentialvalues is not valid in topological dynamics is constructed. Anexample that in topological dynamics for the case of non-abeliangroups, the groups of essential values of cohomologous cocyclesneed not be conjugate is given. A class of base preservingequivariant isomorphisms of Rokhlin cocycle extensions oftopologically transitive flows is described. In particular, thetopological centralizer of Rokhlin cocycle extension of minimalrotation defined by an action of the group ${\mathbb R}^m$ isdetermined.