SHADOWING, EXPANSIVENESS AND STABILITY OF DIVERGENCE-FREE VECTOR FIELDS

Title & Authors
SHADOWING, EXPANSIVENESS AND STABILITY OF DIVERGENCE-FREE VECTOR FIELDS
Ferreira, Celia;

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: $\small{{\bullet}}$ X is a divergence-free vector field satisfying the shadowing property. $\small{{\bullet}}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. $\small{{\bullet}}$ X is an expansive divergence-free vector field. $\small{{\bullet}}$ X has no singularities and is Anosov.
Keywords
Language
English
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4.
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5.
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6.
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