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 (2n − 1)-Kepler problem is proposed.