We propose a unified description for the constants of motion for superintegrable deformations of the oscillator and Coulomb systems on N-dimensional Euclidean space, sphere and hyperboloid. We also consider the duality between these generalized systems and present some example.
@article{arxiv.1612.00794,
title = {Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"},
author = {Tigran Hakobyan and Armen Nersessian and Hovhannes Shmavonyan},
journal= {arXiv preprint arXiv:1612.00794},
year = {2017}
}