Our recent
article: A.Kurov and G.Sardanashvily, “Partially superintegrable systems on Poisson manifolds” in arXiv: 1606.03868
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.
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