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arXiv · 1408.3951

Building Anosov flows on 3-manifolds

François Béguin·Bin Yu·Christian Bonatti
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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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François Béguin, Bin Yu, Christian Bonatti. 2014-08-18. Building Anosov flows on 3-manifolds. https://doi.org/10.2140/gt.2017.21.1837

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