Hénon-Heiles可积系统的Eisenhart提升  

Eisenhart Lift of the Integrable Hénon-Heiles Systems

作　　者：李雯 章海 LI Wen;ZHANG Hai(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2022年第1期82-87,共6页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金青年科学基金项目(11701009)。

摘　　要：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.

关 键 词：可积HAMILTON系统 守恒量 Eisenhart提升 Hénon-Heiles系统 Killing张量 

分 类 号：O411.1[理学—理论物理]