Superintegrable Extensions of Superintegrable Systems - Chanu, C.M.; Degiovanni, L.; Rastelli, G. (Symmetry, Integrability and Geometry: Methods and Applications, 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.