On the Dynamics of Nonreducible Cylindrical Vortices

We study the dynamics of Euclidean isometric extensions of minimal homeomorphisms of compact metric spaces. Under a general hypothesis of homogeneity for the base space, we show that these systems are never minimal, thus extending a classical result of Besicovitch concerning cylindrical cascades. Moreover, using Anosov-Katok-type methods, we construct a topologically transitive isometric extension over an irrational rotation with a two-dimensional fiber.