On the dynamics of non-reducible cylindrical vortices

Details On the dynamics of non-reducible cylindrical vortices On the dynamics of non-reducible cylindrical vortices

2011-01-18

arxiv.org/abs/1101.3526v2

Mathematics

Dynamical Systems

Many minor changes suggested by the referee

Scientific paper

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.

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