
SIGMA 8 (2012), 070, 12 pages arXiv:1210.3126
http://dx.doi.org/10.3842/SIGMA.2012.070
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”
Superintegrable Extensions of Superintegrable Systems
Claudia M. Chanu ^{a}, Luca Degiovanni ^{b} and Giovanni Rastelli ^{c}
^{a)} Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy
^{b)} Formerly at Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy
^{c)} Independent researcher, cna Ortolano 7, Ronsecco, Italy
Received July 30, 2012, in final form September 27, 2012; Published online October 11, 2012
Abstract
A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on E^{2} and S^{2} and for a family of systems defined on constant curvature manifolds. The procedure results effective in many cases including TremblayTurbinerWinternitz and threeparticle Calogero systems.
Key words:
superintegrable Hamiltonian systems; polynomial first integrals.
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