Anomalous Anosov flows revisited

Abstract

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.

26 pages, 3 figures

References in corpus (2)

• Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples
• Algebraic Anosov actions of Nilpotent Lie groups

Cited by in corpus (1)

• Anosov flows in dimension 3 from gluing building blocks with quasi-transverse boundary