  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.
