# A new approach to the higher-order superintegrability of the Tremblay-Turbiner-Winternitz system

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.

Article:

A new approach to the higher-order superintegrability of the Tremblay-Turbiner-Winternitz system

Journal:

J. Phys. A

Volume:

45

Year:

2012

URL:

http://arxiv.org/abs/1211.2919