Shadowing, expansiveness and stability of divergence-free vector fields
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 67-76
https://doi.org/10.4134/BKMS.2014.51.1.67
Printed January 1, 2014
C\'elia Ferreira
Universidade do Porto
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
MSC numbers : 37C50, 37D20, 37C27, 37C10.
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