NON-INTEGRABILITY CRITERION FOR HOMOGENEOUS HAMILTONIAN SYSTEMS VIA BLOWING-UP TECHNIQUE OF SINGULARITIES

被引：0

作者：

Shibayama, Mitsuru ^{[1
]}

机构：

[1] Osaka Univ, Div Math Sci, Grad Sch Engn Sci, Toyonaka, Osaka 5608531, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 08期

关键词：

Integrability; blowing-up technique; homogeneous Hamiltonian systems; ISOSCELES 3-BODY PROBLEM; TRIPLE COLLISION;

D O I：

10.3934/dcds.2015.35.3707

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is a big problem to distinguish between integrable and non-integrable Hamiltonian systems. We provide a new approach to prove the non-integrability of homogeneous Hamiltonian systems with two degrees of freedom. The homogeneous degree can be taken from real values (not necessarily integer). The proof is based on the blowing-up theory which McGehee established in the collinear three-body problem. We also compare our result with Molares-Ramis theory which is the strongest theory in this field.

引用

页码：3707 / 3719

页数：13