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