On Superintegrable Systems with a Cubic Integral of Motion *Supported by the National Natural Science Foundation of China under Grant Nos. 11771352 and 11371293. (January 2018) - Shang 尚, Lin 琳; Huang 黄, Qing 晴
Abstract: We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the associated polynomial Poisson algebras with their algebraic dependence relations are exhibited.