Shadowing, expansiveness and stability of divergence-free vector fields

Details Shadowing, expansiveness and stability of divergence-free vector fields Shadowing, expansiveness and stability of divergence-free vector fields

2010-11-15

arxiv.org/abs/1011.3546v1

Mathematics

Dynamical Systems

Scientific paper

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.

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