Superintegrable systems on Poisson manifolds

24th International Conference on Integrable Systems and Quantum symmetries

Kurov, A.^1 ; Sardanashvily, G.^1

Department of Theoretical Physics, Moscow State University, Moscow

119991, Russia^1

关键词: Action-angle coordinates;    Lie Algebra;    Point wise;    Poisson manifolds;    Poisson structure;    Restrictive conditions;    Symplectic;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/804/1/012025/pdf
DOI  :  10.1088/1742-6596/804/1/012025

来源: IOP

【 摘 要 】

The definition of superintegrable systems on a symplectic manifold 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.