Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system

Abstract

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.

23 pages

References in corpus (6)

• The Poincare'-Lyapounov-Nekhoroshev theorem
• The Liouville-Arnold-Nekhoroshev theorem for non-compact invariant manifolds
• Bi-Hamiltonian partially integrable systems
• Non-commutative Integrability, Moment Map and Geodesic Flows
• Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds
• Noncommutative integrability on noncompact invariant manifolds

Cited by in corpus (2)

• Noether's first theorem in Hamiltonian mechanics
• Partially superintegrable systems on Poisson manifolds