# Partially hyperbolic diffeomorphisms and Lagrangean contact structures

18 Jun 2020 Mion-Mouton Martin IRMA

In this paper, we classify the three-dimensional contact partially hyperbolic diffeomorphisms whose stable, unstable and central distributions are smooth, and whose non-wandering set equals the whole manifold. We prove that up to a finite quotient or a finite power, they are smoothly conjugated either to a time-map of an algebraic contact-Anosov flow, or to an affine partially hyperbolic automorphism of a nil-$\mathrm{Heis}(3)$-manifold... (read more)

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# Categories

• DIFFERENTIAL GEOMETRY
• DYNAMICAL SYSTEMS