On the Stability of Double Homoclinic Loops

被引：0
|
作者：
Clodoaldo Grotta Ragazzo
机构：
[1] (On leave from) Instituto de Matemática e Estatı´stica,
[2] Universidade de São Paulo,undefined
[3] CP 66281,undefined
[4] 05315-970 São Paulo,undefined
[5] SP,undefined
[6] Brazil ,undefined
[7] Department of Mathematics,undefined
[8] Princeton University,undefined
[9] Fine Hall-Washington Road,undefined
[10] Princeton,undefined
[11] NJ 08544-1000,undefined
[12] USA E-mail: ragazzo@math.princeton.edu,undefined
来源：
Communications in Mathematical Physics | 1997年 / 184卷
关键词：
Reflection; Periodic Orbit; Reflection Coefficient; Hamiltonian System; Double Loop;
D O I：
暂无
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学科分类号：
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, ±ν, and pure imaginary eigenvalues, ±ω i). We show that the stability of this double homoclinic loop is determined by the reflection coefficient of a one-dimensional scattering problem and ω/ν. 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.
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页码：251 / 272
页数：21
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