DCDS
Partial hyperbolicity on 3-dimensional nilmanifolds
Andy Hammerlindl
Discrete & Continuous Dynamical Systems - A 2013, 33(8): 3641-3669 doi: 10.3934/dcds.2013.33.3641
Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism. Moreover, if the nilmanifold is not the 3-torus, the center foliation is an invariant circle bundle.
keywords: Partial hyperbolicity classification.
JMD
Integrability and Lyapunov exponents
Andy Hammerlindl
Journal of Modern Dynamics 2011, 5(1): 107-122 doi: 10.3934/jmd.2011.5.107
A smooth distribution, invariant under a dynamical system, integrates to give an invariant foliation, unless certain resonance conditions are present.
keywords: Integrability Lyapunov exponents.
JMD
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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