Building Anosov flows on 3-manifolds

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01056224
Contributor : François Béguin <>
Submitted on : Monday, August 18, 2014 - 11:21:20 AM
Last modification on : Wednesday, February 6, 2019 - 1:24:56 AM
Long-term archiving on : Thursday, November 27, 2014 - 2:05:19 AM

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  • HAL Id : hal-01056224, version 1
  • ARXIV : 1408.3951

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

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