Openness of momentum maps and persistence of extremal relative equilibria

Details Openness of momentum maps and persistence of extremal relative equilibria Openness of momentum maps and persistence of extremal relative equilibria

2002-01-29

arxiv.org/abs/math/0201282v1

Mathematics

Symplectic Geometry

10 pages

Scientific paper

We prove that for every proper Hamiltonian action of a Lie group G in finite dimensions the momentum map is locally G-open relative to its image (i.e. images of G-invariant open sets are open). As an application we deduce that in a Hamiltonian system with continuous Hamiltonian symmetries, extremal relative equilibria persist for every perturbation of the value of the momentum map, provided the isotropy subgroup of this value is compact. We also demonstrate how this persistence result applies to an example of ellipsoidal figures of rotating fluid, and provide an example with plane point vortices which shows how the compactness assumption is related to persistence.

Affiliated with

Also associated with

No associations

Rating

Openness of momentum maps and persistence of extremal relative equilibria 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 Openness of momentum maps and persistence of extremal relative equilibria, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Openness of momentum maps and persistence of extremal relative equilibria will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-627431