Regular and Chaotic Dynamics

, 14:615 | Cite as

Superintegrable system on a sphere with the integral of higher degree

  • A. V. Borisov
  • A. A. Kilin
  • I. S. Mamaev
Research Articles


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 [1], 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 [2] and show that for the latter system an analogous superintegral can be constructed.

Key words

superintegrable systems systems with a potential Hooke center 

MSC2000 numbers

70Hxx 70H06 70G65 37J35 70F10 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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