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Three-dimensional conservative star flows are Anosov

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  • A divergence-free vector field satisfies the star property if any divergence-free vector field in some $C^1$-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 $C^1$-structurally stable three-dimensional conservative flow is Anosov.
    Mathematics Subject Classification: Primary: 37D30; Secondary: 37C75.


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