Canonical transformations map the n-dimensional anisotropic oscillator to the isotropic oscillator, establishing maximal superintegrability for commensurate frequencies with explicit first integrals in 2D.
One can indeed verify that the conserved quantities listed above Po isson-commute with the Hamiltonian of the two-dimensional anisotropic oscillator, which is just I0
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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.