Three-dimensional conservative star flows are Anosov

Bessa, Mário; Rocha, Jorge

http://hdl.handle.net/10400.2/13831

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Authors

Bessa, Mário

Rocha, Jorge

Abstract(s)

A divergence-free vector field satisfies the star property if any divergence-free vector field in some C1-neighborhood has all the singularities and all closed orbits hyperbolic. In this article we prove that any divergence- free star vector field defined in a closed three-dimensional manifold is Anosov. Moreover, we prove that a C1-structurally stable three-dimensional conserva- tive flow is Anosov.