English

Partially superintegrable systems on Poisson manifolds

Mathematical Physics 2017-04-26 v1 math.MP

Abstract

Superintegrable systems on a symplectic manifold conventionally are considered. However, their definition implies a rather restrictive condition 2n=k+m where 2n is a dimension of a symplectic manifold, k is a dimension of a pointwise Lie algebra of a superintegrable system, and m is its corank. To solve this problem, we aim to consider partially superintegrable systems on Poisson manifolds where k+m is the rank of a compatible Poisson structure. The according extensions of the Mishchenko-Fomenko theorem on generalized action-angle coordinates is formulated.

Keywords

Cite

@article{arxiv.1606.03868,
  title  = {Partially superintegrable systems on Poisson manifolds},
  author = {A. Kurov and G. Sardanashvily},
  journal= {arXiv preprint arXiv:1606.03868},
  year   = {2017}
}

Comments

34 pages. arXiv admin note: substantial text overlap with arXiv:1303.5363

R2 v1 2026-06-22T14:23:47.681Z