Superintegrable systems on sphere
| dc.creator | Borisov, A. V. | |
| dc.creator | Mamaev, I. S. | |
| dc.date | 2005-04-07 | |
| dc.date.accessioned | 2026-07-07T05:36:24Z | |
| dc.date.available | 2026-07-07T05:36:24Z | |
| dc.description | We consider various generalizations of the Kepler problem to three-dimensional sphere $S^3$, a compact space of constant curvature. These generalizations include, among other things, addition of a spherical analog of the magnetic monopole (the Poincaré--Appell system) and addition of a more complicated field, which itself is a generalization of the MICZ-system. The mentioned systems are integrable -- in fact, superintegrable. The latter is due to the vector integral, which is analogous to the Laplace--Runge--Lenz vector. We offer a classification of the motions and consider a trajectory isomorphism between planar and spatial motions. The presented results can be easily extended to Lobachevsky space $L^3$. | |
| dc.description | 14 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0504018 | |
| dc.identifier | http://arxiv.org/abs/nlin/0504018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80982 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Superintegrable systems on sphere | |
| dc.type | text |