标题： 一种研究Tremblay-Turbiner-Winternitz系统高阶超可积性的新方法 显示英文标题

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

摘要： 研究了在极坐标下可分离的系统的高阶超可积性，使用了一种之前用于研究广义Smorodinsky-Winternitz系统超可积性的方法。 其思路是，额外的运动常数可以分解为两个特定的较为简单的复函数的幂的乘积（此处分别表示为$M$和$N$）。 该技术导致了Tremblay-Turbiner-Winternitz系统的超可积性的证明以及运动常数的显式表达式。 还研究了与第一类相关的第二类超可积系统。 显示英文摘要

摘要： 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.