Shadowing, expansiveness and stability of divergence-free vector fields
Dynamical Systems
2010-11-17 v1
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: 1. X is in the C1-interior of the set of expansive divergence-free vector fields. 2. X is in the C1-interior of the set of divergence-free vector fields which satisfy the shadowing property. 3. X is in the C1-interior of the set of divergence-free vector fields which satisfy the Lipschitz shadowing property. 4. X has no singularities and X is Anosov.
Keywords
Cite
@article{arxiv.1011.3546,
title = {Shadowing, expansiveness and stability of divergence-free vector fields},
author = {Célia Ferreira},
journal= {arXiv preprint arXiv:1011.3546},
year = {2010}
}