Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system

TL;DR

This paper generalizes the Mishchenko-Fomenko theorem to superintegrable Hamiltonian systems with noncompact invariant submanifolds, exemplified by the Kepler system, and discusses their global action-angle coordinates.

Contribution

It extends the theorem to systems with noncompact invariant submanifolds and analyzes the Kepler system within this framework.

Findings

Kepler system has two types of superintegrable structures

Generalization of Mishchenko-Fomenko theorem to noncompact cases

Existence of global generalized action-angle coordinates

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.