Symmetries and integrals of motion of a superintegrable deformed oscillator
Abstract
The symmetry structure of twodimensional nonlinear isotropic oscillator, introduced in Ballesteros et al. (2008), 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.
- Publication:
-
Annals of Physics
- Pub Date:
- April 2021
- DOI:
- 10.1016/j.aop.2021.168428
- arXiv:
- arXiv:2002.03652
- Bibcode:
- 2021AnPhy.42768428G
- Keywords:
-
- Integrable model;
- Superintegrability;
- Action-angle variables;
- H-J equation;
- Symmetry algebras;
- Deformed oscillator;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics
- E-Print:
- 20 pages, no figures