Action-angle coordinates for integrable systems on Poisson manifolds

Details Action-angle coordinates for integrable systems on Poisson manifolds Action-angle coordinates for integrable systems on Poisson manifolds

2008-05-12

arxiv.org/abs/0805.1679v2

Mathematics

Symplectic Geometry

30 pages, (some improvements done in section 3 and 4 and appendix added in this version)

Scientific paper

We prove the action-angle theorem in the general, and most natural, context of integrable systems on Poisson manifolds, thereby generalizing the classical proof, which is given in the context of symplectic manifolds. The topological part of the proof parallels the proof of the symplectic case, but the rest of the proof is quite different, since we are naturally led to using the calculus of polyvector fields, rather than differential forms; in particular, we use in the end a Poisson version of the classical Caratheodory-Jacobi-Lie theorem, which we also prove. At the end of the article, we generalize the action-angle theorem to the setting of non-commutative integrable systems on Poisson manifolds.

Affiliated with

Also associated with

No associations

Rating

Action-angle coordinates for integrable systems on Poisson manifolds 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 Action-angle coordinates for integrable systems on Poisson manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Action-angle coordinates for integrable systems on Poisson manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-326059