Hénon-Heiles可积系统的Eisenhart提升

Eisenhart Lift of the Integrable Hénon-Heiles Systems

Eisenhart提升是一种产生高维可积系统的有效方法。利用Eisenhart提升方法,通过扩大Hénon-Heiles系统相空间的维数,得到新的高维可积系统。对于Hénon-Heiles系统的三种可积情形和扰动系统,分别推导相应的Hamilton函数、守恒量,验证其可积性,并给出了与新系统相对应的三维Riemann流形上的高阶Killing张量。

Eisenhart lift is an effective approach to generate high-dimensional integrable systems.By using the Eisenhart lift and expanding the phase space of the Hénon-Heiles system,the new higher-dimensional integrable systems is obtained.For the three integrable cases of the Hénon-Heiles system and their perturbations,the corresponding Hamilton functions and integrals of motion are deduced,and their integrability is verified.The higher order Killing tensors on the three-dimensional Riemannian manifolds corresponding to the new systems are given.