Bifurcation of homoclinic orbits to a saddle-center in reversible systems

被引：15

作者：

Klaus, J ^{[1
]}

Knobloch, J ^{[1
]}

机构：

[1] Tech Univ Ilmenau, Dept Math, D-98684 Ilmenau, Germany

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2003年 / 13卷 / 09期

关键词：

reversible system; homoclinic orbit; nonhyperbolic fixed point; bifurcation;

D O I：

10.1142/S0218127403008119

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider two-parameter families of reversible vector fields having (at the critical parameter value) a homoclinic orbit to a nonhyperbolic fixed point. The nonhyperbolicity is due to a pair of purely imaginary eigenvalues. We give a complete description of the bifurcating one-homoclinic orbits to the center manifold. For that purpose we adapt Lin's method.

引用

页码：2603 / 2622

页数：20

共 50 条

[1] Bifurcation of degenerate homoclinic orbits to saddle-center in reversible systems
Liu, Xingbo
Zhu, Deming
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2008, 29 (06) : 575 - 584
[2] Bifurcation of Degenerate Homoclinic Orbits to Saddle-Center in Reversible Systems
Xingbo LIU Deming ZHU Department of Mathematics
[J]. Chinese Annals of Mathematics, 2008, (06) : 575 - 584
[3] Bifurcation of degenerate homoclinic orbits to saddle-center in reversible systems
Xingbo Liu
Deming Zhu
[J]. Chinese Annals of Mathematics, Series B, 2008, 29 : 575 - 584
[4] Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium
Xingbo LIU Xianlong FU Deming ZHU Department of Mathematics
[J]. Chinese Annals of Mathematics, 2007, (01) : 81 - 92
[5] Bifurcation of homoclinic orbits with saddle-center equilibrium
Liu, Xingbo
Fu, Xianlong
Zhu, Deming
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2007, 28 (01) : 81 - 92
[6] Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium*
Xingbo Liu
Xianlong Fu
Deming Zhu
[J]. Chinese Annals of Mathematics, Series B, 2007, 28 : 81 - 92
[7] Action and period of homoclinic and periodic orbits for the unfolding of a saddle-center bifurcation
Diminnie, DC
Haberman, R
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (11): : 3519 - 3530
[8] Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
Qiao, Zhiqin
Xu, Yancong
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
[9] Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium
Liu Xingbo
[J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (04) : 409 - 416
[10] On Hamiltonian Systems with a Homoclinic Orbit to a Saddle-Center
O. Yu. Koltsova
[J]. Journal of Mathematical Sciences, 2005, 128 (2) : 2787 - 2790

← 1 2 3 4 5 →