Abstract
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:
We build a closed three-dimensional manifold supporting both a transitive Anosov vector field and a nontransitive Anosov vector field.
For any , we build a closed three-dimensional manifold supporting at least pairwise different Anosov vector fields.
We build transitive hyperbolic attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive hyperbolic attractors.
We build a transitive Anosov vector field admitting infinitely many pairwise nonisotopic transverse tori.
Citation
François Béguin. Christian Bonatti. Bin Yu. "Building Anosov flows on $3$–manifolds." Geom. Topol. 21 (3) 1837 - 1930, 2017. https://doi.org/10.2140/gt.2017.21.1837
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