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VOL. 16 | 2015 On the Trajectories of U(1)-Kepler Problems
Guowu Meng

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

## Abstract

The classical $\mathrm{U}(1)$-Kepler problems at level $n\ge 2$ were formulated, and their trajectories are determined via an idea similar to the one used by Kustaanheimo and Stiefel in the study of Kepler problem. It is found that a non-colliding trajectory is an ellipse, a parabola or a branch of hyperbola according as the total energy is negative, zero or positive, and the complex orientation-preserving linear automorphism group of $\mathbb C^n$ acts transitively on both the set of elliptic trajectories and the set of parabolic trajectories.

## Information

Published: 1 January 2015
First available in Project Euclid: 13 July 2015

zbMATH: 1352.53071
MathSciNet: MR3363847

Digital Object Identifier: 10.7546/giq-16-2015-219-230