# SHADOWING, EXPANSIVENESS AND STABILITY OF DIVERGENCE-FREE VECTOR FIELDS

• Ferreira, Celia
• Published : 2014.01.31
• 61 5

#### Abstract

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: ${\bullet}$ X is a divergence-free vector field satisfying the shadowing property. ${\bullet}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. ${\bullet}$ X is an expansive divergence-free vector field. ${\bullet}$ X has no singularities and is Anosov.

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