Symmetries and integrals of motion of a superintegrable deformed oscillator
arXiv:2002.03652 · doi:10.1016/j.aop.2021.168428
Abstract
The symmetry structure of twodimensional nonlinear isotropic oscillator, introduced in Physica D237 (2008) 505, is discussed. It is shown that it possesses three independent integrals of motion which can be chosen in such a way that they span SU(2), E(2) or SU(1,1) algebras, depending on the value of total energy. They generate the infinitesimal canonical symmetry transformations; integrability of the latter is analyzed. The results are then generalized to the case of arbitrary number of degrees of freedom.
20 pages, no figures; version which appeared in Annals of Physics (except two sentences of explanation added here)