Building Anosov flows on 3–manifolds

By Franccois B'eguin, Bin Yu, C. Bonatti. 2014

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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 transverse tori. MSC 2010: 37D20, 57M. Keywords: Anosov flow, hyperbolic basic set, 3-manifold.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

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