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      Structure theory for second order 2D superintegrable systems with 1-parameter potentials

      Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr.; Post, Sarah
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      sigma09-008.pdf
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      DOI
       10.3842/SIGMA.2009.008
      Link
       www.emis.de
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      Kalnins, E. G., Kress, J. M., Miller, W., Jr. & Post, S. (2009). Structure theory for second order 2D superintegrable systems with 1-parameter potentials. Symmetry, Integrability and Geometry: Methods and Applications, 5, 008.
      Permanent Research Commons link: https://hdl.handle.net/10289/3547
      Abstract
      The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is Stäckel equivalent to a system on a constant curvature space.
      Date
      2009
      Type
      Journal Article
      Rights
      This article has been published in the journal: Symmetry, Integrability and Geometry: Methods and Applications. Used with permission.
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      • Computing and Mathematical Sciences Papers [1457]
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