Three superintegrable two-dimensional oscillators:: Superintegrability, nonlinearity, and curvature

The superintegrability of three different two-dimensional oscillators is studied: (i) a nonlinear oscillator dependent on a parameter lambda (two-dimensional version of the oscillator of Lakshmanan and Mathews), (ii) a nonlinear oscillator related to the Riccati equation, and (iii) the standard harmonic oscillator on constant curvature spaces. They can be considered as nonlinear deformations, or curvature-dependent versions, of the linear harmonic oscillator.