MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (S1): 105-113.

MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE

曾唯尧¹, 周玉波², 张卫国¹

1. Department of Mathematics, Changsha Railway University, Changsh 410045, China;
2. Departmetn of Mathematics. Hunan Mormal University

收稿日期:1996-07-01 修回日期:1997-04-14 出版日期:1998-12-31 发布日期:1998-12-31
基金资助:
This work is supported by NSF of China

MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE

Zeng weiyao¹, Zhou Yubo², Zhang Weiguo¹

1. Department of Mathematics, Changsha Railway University, Changsh 410045, China;
2. Departmetn of Mathematics. Hunan Mormal University

Received:1996-07-01 Revised:1997-04-14 Online:1998-12-31 Published:1998-12-31
Supported by:
This work is supported by NSF of China

摘要/Abstract

摘要： The main purpose of this paper is to study homocliaic bifurcation in a degenerate case of differential equations of form x=f(x, ε) and x=g(x) + h(t, x. ε). By using theory of exponential dichotomies and Liapunov-Schmidt method, the authors obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.

关键词: Exponential dichotomies, Liapunov-Schmidt method, Homoclinic orbits

Abstract: The main purpose of this paper is to study homocliaic bifurcation in a degenerate case of differential equations of form x=f(x, ε) and x=g(x) + h(t, x. ε). By using theory of exponential dichotomies and Liapunov-Schmidt method, the authors obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.

Key words: Exponential dichotomies, Liapunov-Schmidt method, Homoclinic orbits

曾唯尧, 周玉波, 张卫国. MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE[J]. 数学物理学报(英文版), 1998, 18(S1): 105-113.

Zeng weiyao, Zhou Yubo, Zhang Weiguo. MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE[J]. Acta mathematica scientia,Series B, 1998, 18(S1): 105-113.

[1]	万莉莉, 唐春雷. HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS[J]. 数学物理学报(英文版), 2010, 30(1): 312-318.
[2]	曾唯尧, 钱祥征, 王志成. EXPONENTIAL DICHOTOMIES,HOMOCLINIC ORBITS AND METHODS OF MELNIKOV[J]. 数学物理学报(英文版), 1996, 16(1): 113-120.

MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE

MELNIKOV VECTOR AND HOMOCLINIC BIFURCATIONS IN A DEGENERATE CASE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

Metrics

本文评价

推荐阅读 10