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SHADOWING, EXPANSIVENESS AND STABILITY OF DIVERGENCE-FREE VECTOR FIELDS

  • Ferreira, Celia
  • Received : 2012.05.31
  • Published : 2014.01.31

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.

Keywords

shadowing;Lipschitz shadowing;expansiveness;Anosov vector fields

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