Non-integrability of Henon-Heiles system

被引：12
|
作者：
Li, Wenlei [1 ]
Shi, Shaoyun [2 ]
机构：
[1] Jilin Univ, Coll Math, Changchun 130012, Peoples R China
[2] Jilin Univ, Minist Educ, Key Lab Symbol Computat & Knowledge Engn, Changchun 130012, Peoples R China
来源：
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2011年 / 109卷 / 01期
关键词：
Non-integrability; Henon-Heiles system; Morales-Ramis theory; Lame equation; Higher order variational equations; HAMILTONIAN-SYSTEMS; VARIATIONAL EQUATIONS; INTEGRABILITY;
D O I：
10.1007/s10569-010-9315-1
中图分类号：
P1 [天文学];
学科分类号：
0704 ;
摘要：
We show that the H,non-Heiles system with Hamiltonian H = 1/2(y(1)(2) + y(2)(2)) + 1/2(ax(1)(2) + bx(2)(2)) + 1/3dx(2)(3) + cx(1)(2)x(2) is integrable in Liouvillian sense (i.e., the existence of an additional first integral) if and only if c = 0; or d/c = 1, a = b; or d/c = 6, a, b arbitrary; or d/c = 16, b = 16a. Therefore, we get a complete classification of the H,non-Heiles system in sense of integrability and non-integrability.
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页码：1 / 12
页数：12
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