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Classification of partially hyperbolic diffeomorphisms under some rigid conditions

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arxiv 1903.09264 v4 pith:UOA7HPJU submitted 2019-03-21 math.DS

Pablo D. Carrasco , Enrique Pujals , Federico Rodriguez-Hertz This is my paper · ORCID
classification math.DS
keywords anosovclassificationdiffeomorphismhyperbolicpartiallyrigidsomeunder
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Consider a three dimensional partially hyperbolic diffeomorphism. It is proven that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) either an Anosov diffeomorphism, a skew-product or the time-one map of an Anosov flow, thus recovering a well known classification conjecture of the second author to this restricted setting.

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  1. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case

    math.DS 2019-08 conditional novelty 8.0 of 10

    On hyperbolic and Seifert fibered 3-manifolds, dynamically coherent partially hyperbolic diffeomorphisms homotopic to the identity are, up to iterate, leaf conjugate to time-one maps of topological Anosov flows.

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