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Pré-Publication, Document De Travail Année : 2014

Building Anosov flows on 3-manifolds

Bin Yu
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Résumé

We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting both of a transitive Anosov vector field and a non-transitive Anosov vector field; 2. for any n, we build a 3-manifold M supporting at least n pairwise different Anosov vector fields; 3. we build transitive attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive attractors; 4. we build a transitive Anosov vector field admitting infinitely many pairwise non-isotopic trans- verse tori.
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Dates et versions

hal-01056224 , version 1 (18-08-2014)

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François Béguin, Bin Yu, Christian Bonatti. Building Anosov flows on 3-manifolds. 2014. ⟨hal-01056224⟩
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