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.

7 pages

References in corpus (2)

• Multi-center MICZ-Kepler system, supersymmetry and integrability
• Dipole transitions and Stark effect in the charge-dyon system

Cited by in corpus (12)

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• Bertrand spacetimes as Kepler/oscillator potentials
• Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds
• A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane
• Remarks on Multi-Dimensional Conformal Mechanics
• 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
• Superintegrable deformations of oscillator and Coulomb systems
• Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials
• Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid