Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 070, 12 pages      arXiv:1210.3126
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

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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