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 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.2014.51.1.67Printed 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. Downloads: Full-text PDF