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

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Cited by in corpus (9)

• Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
• The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
• Extensions of Hamiltonian systems dependent on a rational parameter
• Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials
• On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces
• Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System
• Extended Hamiltonians and shift, ladder functions and operators
• Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion
• Extensions of non-natural Hamiltonians