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Partially hyperbolic diffeomorphisms and Lagrangian contact structures
Published online by Cambridge University Press: 12 November 2021
Abstract
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In this paper, we classify the three-dimensional partially hyperbolic diffeomorphisms whose stable, unstable, and central distributions 
$E^s$, 
$E^u$, and 
$E^c$ are smooth, such that 
$E^s\oplus E^u$ is a contact distribution, 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. The rigid geometric structure induced by the invariant distributions plays a fundamental part in the proof.
Keywords
MSC classification
Secondary:
53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
53C30: Homogeneous manifolds
37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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- © The Author(s), 2021. Published by Cambridge University Press
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