Abstract
Two important advances in integrability have been the recent discovery of the higher-order superintegrability of the Tremblay–Turbiner–Winternitz system (related to the harmonic oscillator) and the Post–Winternitz system (related to the Kepler problem). The properties of the TTW system have been recently studied on the two-dimensional spherical Sκ2 (κ>0) and hyperbolic Hκ2 (κ<0) spaces by making use of a curvature-dependent formalism and the existence of a complex factorization for the higher-order constant of motion. Now in this Letter we prove that a similar technique can also be applied for the study of the PW system.
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