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 2-dimensional fiber. MSC: 37B05, 37E30, 37F50,
['Daniel Coronel', 'Andrés Navas', 'Mario Ponce']
On the dynamics of nonreducible cylindrical vortices