Perturbed (2𝑛 − 1)-Dimensional Kepler Problem and the Nilpotent Adjoint Orbits of 𝑈(𝑛, 𝑛)

Abstract

We study the regularized (2𝑛 − 1)-Kepler problem and other Hamiltonian systems which are related to the nilpotent coadjoint orbits of 𝑈(𝑛, 𝑛). The Kustaanheimo-Stiefel and Cayley regularization procedures are discussed, and their equivalence is shown. Some integrable generalization (perturbation) of the (2𝑛 − 1)-Kepler problem is proposed.