Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
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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 $\cosθ$ 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
7 pages