The higher-order superintegrability of systems separable in polar coordinates is studied using an approch that was previously applied for the study of the superintegrability of a generalized Smorodinsky-Winternitz system. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by $M$ and $N$). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system and to the explicit expression of the constants of motion. A second family (related with the first one) of superintegrable systems is also studied.
Higher-order superintegrability of separable potentials with a new approach to the Post-Winternitz system
The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
A new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearities
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