  Performing the Hamiltonian analysis we explicitly established the canonical
equivalence of the deformed oscillator, constructed in
arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence,
we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary
two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry
is a non-polynomial structure of its generators written it terms of the
oscillator variables.
