HIGHER-ORDER MELNIKOV METHOD AND CHAOS FOR TWO-DEGREE-OF-FREEDOM HAMILTONIAN SYSTEMS WITH SADDLE-CENTERS

被引：4

作者：

Yagasaki, Kazuyuki ^{[1
]}

机构：

[1] Gifu Univ, Dept Mech & Syst Engn, Gifu 5011193, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 29卷 / 01期

关键词：

Melnikov method; chaos; Smale horseshoe; Hamiltonian system; saddle-center; Henon-Heiles system; 1ST INTEGRALS; ORBITS;

D O I：

10.3934/dcds.2011.29.387

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider two-degree-of-freedom Hamiltonian systems with saddle-centers, and develop a Melnikov-type technique for detecting creation of transverse homoclinic orbits by higher-order terms. We apply the technique to the generalized Henon-Heiles system and give a positive answer to a remaining question of whether chaotic dynamics occurs for some parameter values although it is known to be nonintegrable in a complex analytical meaning.

引用

页码：387 / 402

页数：16

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