On algebraic construction of certain integrable and super-integrable systems |
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| Authors: | AJ Maciejewski M Przybylska |
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| Institution: | a J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra, Polandb Institute of Physics, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra, Polandc St. Petersburg State University, St. Petersburg, Russia |
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| Abstract: | We propose a new construction of two-dimensional natural bi-Hamiltonian systems associated with a very simple Lie algebra. The presented construction allows us to distinguish three families of super-integrable monomial potentials for which one additional first integral is quadratic, and the second one can be of arbitrarily high degree with respect to the momenta. Many integrable systems with additional integrals of degree greater than two in momenta are given. Moreover, an example of a super-integrable system with first integrals of degree two, four and six in the momenta is found. |
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| Keywords: | Super-integrability Bi-Hamiltonian systems Poisson manifold Hypergeometric function Separation of variables |
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