On the dynamics of non-reducible cylindrical vortices
Dynamical Systems
2014-02-26 v2
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.
Keywords
Cite
@article{arxiv.1101.3526,
title = {On the dynamics of non-reducible cylindrical vortices},
author = {D. Coronel and A. Navas and M. Ponce},
journal= {arXiv preprint arXiv:1101.3526},
year = {2014}
}
Comments
Many minor changes suggested by the referee