SIGMA 8 (2012), 070, 12 pages      arXiv:1210.3126      https://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 E² and S² and for a family of systems defined on constant curvature manifolds. The procedure results effective in many cases including Tremblay-Turbiner-Winternitz and three-particle Calogero systems.

Key words: superintegrable Hamiltonian systems; polynomial first integrals.

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References

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