ИСТИНА

Superintegrable (non-commutative completely integrable) 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, partially superintegrable systems on Poisson manifolds in the presence of different compatible Poisson structures are studied. The according extensions of the Mishchenko--Fomenko theorem on generalized action-angle coordinates (Theorem 6) can be proved.