Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

Abstract

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos \theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.

arXiv comment7 pages

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• The anisotropic oscillator on curved spaces: A new exactly solvable model
• Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
• A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane
• The Coulomb problem on a 3-sphere and Heun polynomials
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Remarks on Multi-Dimensional Conformal Mechanics
• Factorization approach to superintegrable systems: Formalism and applications
• Curvature as an integrable deformation
• Action-Angle Variables In Conformal Mechanics
• Anisotropic Higgs oscillator
• 16D anisotropic inharmonic oscillator and 9D related (MICZ-)Kepler-like systems
• Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid
• Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials
• Superintegrable deformations of oscillator and Coulomb systems