New superintegrable system on a sphere
A. V. Borisov, A. A. Kilin, I. S. Mamaev
Institute of Computer Science
We consider the motion of a material point on the surface of a sphere in the field of $2n+1$ identical Hooke centers (singularities with elastic potential) lying on a great circle. Our main result is that this system is superintegrable. The property of superintegrability for this system has been conjectured by us in , where the structure of a superintegral of arbitrarily high odd degree in momemnta was outlined. We also indicate an isomorphism between this system and the one-dimensional $N$-particle system discussed in the recent paper  and show that for the latter system an analogous superintegral can be constructed.
superintegrable systems, systems with a potential, Hooke center.
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MSC: 70Hxx, 70H06, 70G65, 37J35, 70F10
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “New superintegrable system on a sphere”, Nelin. Dinam., 5:4 (2009), 455–462
Citation in format AMSBIB
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper New superintegrable system on a sphere
\jour Nelin. Dinam.
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