2014/08/18 by François Béguin, Bin Yu, Christian Bonatti · 34 citations
Computer Science · Mathematics · #Cellular Automata and Applications #Field (mathematics) #Geometric and Algebraic Topology #Hyperbolic manifold #Hyperbolic set #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Pairwise comparison #Transitive relation #Vector bundle #Vector field #math.DS
paper · pdf · doi:10.2140/gt.2017.21.1837
published in Geometry & Topology 21(3), 1837-1930 (Mathematical Sciences Publishers) · 58 pages
arxiv created 2014/08/18 · openalex created_date 2016/06/24 · openalex publication_date 2017/05/10 · arxiv updated 2017/06/14 · openalex updated_date 2026/08/05
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: ¶\n<ol>\n<li>We build a closed three-dimensional manifold supporting both a transitive Anosov vector field and a nontransitive Anosov vector field. </li>\n<li>For any [math] , we build a closed three-dimensional manifold [math] supporting at least [math] pairwise different Anosov vector fields. </li>\n<li>We build transitive hyperbolic attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive hyperbolic attractors. </li>\n<li>We build a transitive Anosov vector field admitting infinitely many pairwise nonisotopic transverse tori.</li>\n</ol>