Partially hyperbolic diffeomorphisms and Lagrangian contact structures
Keyword(s):
Abstract 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.
2016 ◽
Vol 38
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pp. 401-443
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2011 ◽
Vol 32
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pp. 825-839
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2014 ◽
Vol 35
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pp. 412-430
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2005 ◽
Vol 84
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pp. 1693-1715
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2016 ◽
Vol 38
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pp. 384-400
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2016 ◽
Vol 434
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pp. 1123-1137
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2008 ◽
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pp. 843-862
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