Superintegrable Extensions of Superintegrable Systems
  A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on $\mathbb E^2$ and $\mathbb S^2$ 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. 
Claudia M. Chanu, Luca Degiovanni and Giovanni Rastelli
math-ph math.MP nlin.SI