On the stability of double homoclinic loops

被引：19
|
作者：
Ragazzo, CG
机构：
[1] PRINCETON UNIV,DEPT MATH,PRINCETON,NJ 08544
[2] NYU,COURANT INST MATH SCI,NEW YORK,NY
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1997年 / 184卷 / 02期
关键词：
D O I：
10.1007/s002200050060
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider 2-degrees of freedom Hamiltonian systems with an involutive symmetry and a pair of orbits bi-asymptotic (homoclinic) to a saddle-center equilibrium (related to pairs of pure real, +/-nu, and pure imaginary eigenvalues, +/-omega i). We show that the stability of this double homoclinic loop is determined by the reflection coefficient of a one-dimensional scattering problem and omega/nu. We also show that the mechanism for losing stability is the creation of an infinite heteroclinic chain connecting a sequence of periodic orbits that accumulates at the double loop.
引用
收藏
页码：251 / 272
页数：22
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