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

Symmetry Integrability and Geometry-Methods and Applications

article

Anatol Odzijewicz¹ 

[1] Department of Mathematics, University of Białystok

关键词: integrable Hamiltonian systems;    Kepler problem;    nonlinear differential equations;    symplectic geometry;    Poisson geometry;    Kustaanheimo–Stiefel transformation;    celestial mechanics 2020 Mathematics Subject Classification 53D17;    53D20;    53D22;    70H06;   

DOI  :  10.3842/SIGMA.2020.087

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown