Narrow Results

The Mishchenko–Fomenko theorem on superintegrable Hamiltonian systems is generalized to superintegrable Hamiltonian systems with noncompact invariant submanifolds. It is formulated in the case of globally superintegrable Hamiltonian systems which admit global generalized action-angle coordinates. The well known Kepler system falls into two different globally superintegrable systems with compact and noncompact invariant submanifolds.

The Mishchenko–Fomenko theorem on action-angle coordinates is extended to time-dependent superintegrable Hamiltonian systems.