Superintegrable Extensions of Superintegrable Systems

Abstract

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.

This article recollects results published in arXiv:1101.5975 and applies them in a new context

References in corpus (3)

• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Superintegrable 3-body systems on the line
• Tools for Verifying Classical and Quantum Superintegrability