Canonical transformations map the n-dimensional anisotropic oscillator to the isotropic oscillator, establishing maximal superintegrability for commensurate frequencies with explicit first integrals in 2D.
Marquette, Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems , J
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Dynamical symmetries of the anisotropic oscillator
Canonical transformations map the n-dimensional anisotropic oscillator to the isotropic oscillator, establishing maximal superintegrability for commensurate frequencies with explicit first integrals in 2D.