Bull. Korean Math. Soc. 2014; 51(1): 67-76
Printed January 1, 2014
https://doi.org/10.4134/BKMS.2014.51.1.67
Copyright © The Korean Mathematical Society.
C\'elia Ferreira
Universidade do Porto
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.
2022; 59(2): 481-506
2013; 50(5): 1495-1499
2003; 40(4): 703-713
2006; 43(1): 43-52
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd