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Article Dans Une Revue Geometry and Topology Année : 2017

Building Anosov flows on $3$–manifolds

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Résumé

We prove we can build (transitive or nontransitive) Anosov flows on closed three-dimensional manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications of this result; for example: (1) We build a closed three-dimensional manifold supporting both a transitive Anosov vector field and a nontransitive Anosov vector field. (2) For any $n$ , we build a closed three-dimensional manifold $M$ supporting at least $n$ pairwise different Anosov vector fields. (3) We build transitive hyperbolic attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive hyperbolic attractors. (4) We build a transitive Anosov vector field admitting infinitely many pairwise nonisotopic transverse tori.

Dates et versions

hal-01565095 , version 1 (19-07-2017)

Identifiants

Citer

François Béguin, Christian Bonatti, Bin Yu. Building Anosov flows on $3$–manifolds. Geometry and Topology, 2017, 21 (3), pp.1837 - 1930. ⟨10.2140/gt.2017.21.1837⟩. ⟨hal-01565095⟩
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