Reduction of superintegrable systems: the anisotropic harmonic oscillator

TL;DR

This paper introduces a new family of maximally superintegrable systems derived from an anisotropic harmonic oscillator, featuring polynomial integrals of motion and closed orbits, expanding the class of known superintegrable models.

Contribution

It presents a novel 2N-parametric family of superintegrable systems in N dimensions obtained via reduction, generalizing existing models with polynomial integrals of motion.

Findings

Systems have closed bounded orbits

Possess polynomial integrals of motion

Generalize known superintegrable models

Abstract

We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional configuration space. These systems possess closed bounded orbits and integrals of motion which are polynomial in the momenta. They generalize known examples of superintegrable models in the Euclidean plane.