Superintegrable systems on Poisson manifolds

Abstract

Abstract. 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.