On the dynamics of nonreducible cylindrical vortices
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Date
2012
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Publisher
OXFORD UNIV PRESS
Abstract
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.
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Keywords
TRANSFORMATIONS, SYSTEMS