Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 087, 23 pages      arXiv:1806.05912      https://doi.org/10.3842/SIGMA.2020.087

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

Anatol Odzijewicz
Department of Mathematics, University of Białystok,Ciołkowskiego 1M, 15-245 Białystok, Poland

Received March 11, 2020, in final form September 01, 2020; Published online September 22, 2020

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.

Key words: integrable Hamiltonian systems; Kepler problem; nonlinear differential equations; symplectic geometry; Poisson geometry; Kustaanheimo-Stiefel transformation; celestial mechanics.

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