Building Anosov flows on 3-manifolds

Francois Beguin Christian Bonatti Bin Yu

Dynamical Systems mathscidoc:1907.11001

Best Paper Award in 2019

Geometry and Topology, 21, (3), 1837-1930, 2017.5
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: 1.We build a closed three-dimensional manifold supporting both a transitive Anosov vector field and a nontransitive Anosov vector field. 2.For any n, we build a closed three-dimensional manifold M supporting at least n pairwise different Anosov vector fields. 3.We build transitive hyperbolic attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive hyperbolic attractors. 4.We build a transitive Anosov vector field admitting infinitely many pairwise nonisotopic transverse tori.
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@inproceedings{francois2017building,
  title={Building Anosov flows on 3-manifolds},
  author={Francois Beguin, Christian Bonatti, and Bin Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190705163021343457398},
  booktitle={Geometry and Topology},
  volume={21},
  number={3},
  pages={1837-1930},
  year={2017},
}
Francois Beguin, Christian Bonatti, and Bin Yu. Building Anosov flows on 3-manifolds. 2017. Vol. 21. In Geometry and Topology. pp.1837-1930. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190705163021343457398.
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