Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"

TL;DR

This paper introduces a unified framework for understanding constants of motion in superintegrable deformations of oscillator and Coulomb systems across various geometries, highlighting dualities and holomorphic structures.

Contribution

It provides a novel unified description of constants of motion and explores dualities in superintegrable deformations of classical systems on different geometries.

Findings

Unified description of constants of motion for deformed systems

Identification of dualities between oscillator and Coulomb systems

Examples illustrating the generalized systems and their properties

Abstract

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.