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

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.

12 pages

References in corpus (6)

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• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Particle dynamics near extreme Kerr throat and supersymmetry
• Lobachevsky geometry of (super)conformal mechanics
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Cited by in corpus (5)

• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Quasi-exactly solvable extensions of the Kepler-Coulomb potential on the sphere
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Superintegrability of 3-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems
• Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$