Stability properties of divergence-free vector fields

Details Stability properties of divergence-free vector fields Stability properties of divergence-free vector fields

2010-04-16

arxiv.org/abs/1004.2893v2

Mathematics

Dynamical Systems

24 pages

Scientific paper

A divergence-free vector field satisfies the star property if any divergence-free vector field in some C1-neighborhood has all singularities and all periodic orbits hyperbolic. In this paper we prove that any divergence-free vector field defined on a Riemannian manifold and satisfying the star property is Anosov. It is also shown that a C1-structurally stable divergencefree vector field can be approximated by an Anosov divergence-free vector field. Moreover, we prove that any divergence-free vector field can be C1-approximated by an Anosov divergence-free vector field, or else by a divergence-free vector field exhibiting a heterodimensional cycle.

Affiliated with

Also associated with

No associations

Rating

Stability properties of divergence-free vector fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability properties of divergence-free vector fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability properties of divergence-free vector fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-624465