DCDS
Partial hyperbolicity on 3-dimensional nilmanifolds
Andy Hammerlindl
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
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

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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