Superintegrable Extensions of Superintegrable Systems

[摘要] 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 Tremblay-Turbiner-Winternitz and three-particle Calogero systems.

[关键词] superintegrable Hamiltonian systems;polynomial first integrals