Partially hyperbolic diffeomorphisms with a trapping property
Rafael Potrie
Discrete & Continuous Dynamical Systems - A 2015, 35(10): 5037-5054 doi: 10.3934/dcds.2015.35.5037
We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.
keywords: quasi-attractors classification Partial hyperbolicity dynamical coherence.
Seifert manifolds admitting partially hyperbolic diffeomorphisms
Andy Hammerlindl Rafael Potrie Mario Shannon
Journal of Modern Dynamics 2018, 12(1): 193-222 doi: 10.3934/jmd.2018008

We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.

keywords: Partially hyperbolic diffeomorphisms Seifert spaces

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