On the dynamics of non-reducible cylindrical vortices

Abstract

We study skew-maps given by a minimal homeomorphism on the basis and a cocycle of affine isometries on the fibers. We call such a map a cylindrical vortex. We extend to this setting some classical results of Atkinson, Besicovitch, Matsumoto-Shishikura and Schinelman (among other people) about cylindrical cascades. In particular, we show that no cylindrical vortex is minimal, and we construct interesting examples of topologically transitive ones.

Many minor changes suggested by the referee