%0 Journal Article %T Building Anosov flows on $3$–manifolds %+ Laboratoire Analyse, Géométrie et Applications (LAGA) %+ Institut de Mathématiques de Bourgogne [Dijon] (IMB) %+ School of Mathematical Sciences [Shanghai] %A Béguin, François %A Bonatti, Christian %A Yu, Bin %Z National Natural Science Foundation of China - NSFC 11471248 %< avec comité de lecture %@ 1465-3060 %J Geometry and Topology %I Mathematical Sciences Publishers %V 21 %N 3 %P 1837 - 1930 %8 2017 %D 2017 %Z 1408.3951 %R 10.2140/gt.2017.21.1837 %K Anosov flows %K 3–manifolds %K Hyperbolic plugs %K Diffeomorphisms %K Manifolds %K Foliations %Z MSC: Primary: 37D20 Secondary: 57M99 %Z Mathematics [math]Journal articles %X 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. %G English %L hal-01565095 %U https://u-bourgogne.hal.science/hal-01565095 %~ UNIV-PARIS13 %~ UNIV-BOURGOGNE %~ UNIV-PARIS8 %~ CNRS %~ LAGA %~ INSMI %~ IMB_UMR5584 %~ USPC %~ GALILE %~ UNIV-PARIS-LUMIERES %~ SORBONNE-PARIS-NORD %~ UNIV-PARIS8-OA