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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 087, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.087 (Mi sigma1624) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2020.087
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.
Keywords: integrable Hamiltonian systems, Kepler problem, nonlinear differential equations, symplectic geometry, Poisson geometry, Kustaanheimo–Stiefel transformation, celestial mechanics.
Received: March 11, 2020; in final form September 1, 2020; Published online September 22, 2020
Bibliographic databases:
Document Type: Article
MSC: 53D17, 53D20, 53D22, 70H06
Language: English
Citation: Anatol Odzijewicz, “Perturbed $(2n-1)$-Dimensional Kepler Problem and the Nilpotent Adjoint Orbits of $U(n, n)$”, SIGMA, 16 (2020), 087, 23 pp.
Citation in format AMSBIB
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\paper Perturbed $(2n-1)$-Dimensional Kepler Problem and the Nilpotent Adjoint Orbits of $U(n, n)$
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\vol 16
\papernumber 087
\totalpages 23
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