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Superintegrable systems on sphere | | A.V. Borisov
; I.S. Mamaev
; | | Date: |
7 Apr 2005 | | Subject: | Exactly Solvable and Integrable Systems; Chaotic Dynamics | nlin.SI nlin.CD | | Abstract: | 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 $L^3$. | | Source: | arXiv, nlin.SI/0504018 | | Services: | Forum | Review | PDF | Favorites | |
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