Building Anosov flows on $3$–manifolds

Abstract : 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.
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Geometry and Topology, Mathematical Sciences Publishers, 2017, 21 (3), pp.1837 - 1930. 〈10.2140/gt.2017.21.1837〉
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01565095
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mercredi 19 juillet 2017 - 14:40:02
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

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

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