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arXiv · 1004.2893

Stability properties of divergence-free vector fields

Célia Ferreira
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Abstract

A divergence-free vector field satisfies the star property if any divergence-free vector field in some C1-neighborhood has all singularities and all periodic orbits hyperbolic. In this paper we prove that any divergence-free vector field defined on a Riemannian manifold and satisfying the star property is Anosov. It is also shown that a C1-structurally stable divergencefree vector field can be approximated by an Anosov divergence-free vector field. Moreover, we prove that any divergence-free vector field can be C1-approximated by an Anosov divergence-free vector field, or else by a divergence-free vector field exhibiting a heterodimensional cycle.

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Célia Ferreira. 2011-03-03. Stability properties of divergence-free vector fields. https://arxiv.org/abs/1004.2893

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