Ergodic continuous skew product actions of amenable groups (Q1057386)

Given two compact, metric topological dynamical systems (Y,T,\(\mu)\) and (Z,G,\(\nu)\), where T and G are locally compact separable groups acting continuously on spaces, preserving finite ergodic measures \(\mu\) and \(\nu\) respectively, a continuous cocycle \(\alpha\) on (Y,T,\(\mu)\) defines a skew product T action on \(Z\times Y\) by \((z,y)\cdot t\to (z\alpha (y,t),y\cdot t).\) We prove that for a large class of amenable groups T and, under some very general conditions on spaces Y, Z and G, residually many continuous cocycles lift various ergodic and mixing properties from Y to \(Z\times Y\). Similar results are obtained for non-trivial compact group extensions of (Y,T,\(\mu)\).