Superintegrable system on a sphere with the integral of higher degree
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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.
Key wordssuperintegrable systems systems with a potential Hooke center
MSC2000 numbers70Hxx 70H06 70G65 37J35 70F10
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