6533b825fe1ef96bd1283301
RESEARCH PRODUCT
Building Anosov flows on $3$–manifolds
Bin YuChristian BonattiFrançois Béguinsubject
[ MATH ] Mathematics [math]Pure mathematicsAnosov flowMathematics::Dynamical Systems3–manifolds[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)$3$–manifolds01 natural sciencesFoliationsSet (abstract data type)MSC: Primary: 37D20 Secondary: 57M9957M99Diffeomorphisms0103 physical sciencesAttractorFOS: Mathematics0101 mathematics[MATH]Mathematics [math]Mathematics - Dynamical SystemsManifoldsMathematics::Symplectic Geometry3-manifold37D20 57MMathematicsTransitive relation37D20010308 nuclear & particles physics010102 general mathematicsTorusMathematics::Geometric TopologyFlow (mathematics)Anosov flowsFoliation (geology)Vector fieldhyperbolic plugsGeometry and Topologyhyperbolic basic set3-manifolddescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-08-18 |