| Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition |
| |
| 作者姓名： | De Ming ZHU Ying SUN |
| |
| 作者单位： | [1]Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China [2]School of Science, University of Ji＇nan, Ji＇nan 250022, P. R. China |
| |
| 基金项目： | Project supported by NNSFC under Grant 10371040 and NNSFC under Grant 10371040 and Jinan University Research Funds for Doctors （B0636） |
| |
| 摘 要： | In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.
|
| 关 键 词： | 可逆条件 周期轨道 Poincare映射 鞍点 |
| 收稿时间： | 4 April 2005 |
| 修稿时间： | 2005-04-04 |
Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle–focus and Saddle Under Reversible Condition |
| |
| De Ming ZHU Ying SUN.Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition[J].Acta Mathematica Sinica,2007,23(8):1495-1504. |
| |
| Authors: | De Ming Zhu Ying Sun |
| |
| Institution: | (1) Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China;(2) School of Science, University of Ji'nan, Ji'nan 250022, P. R. China |
| |
| Abstract: | In this paper, we study the dynamical behavior for a 4–dimensional reversible system near its heteroclinic loop connecting
a saddle–focus and a saddle. The existence of infinitely many reversible 1–homoclinic orbits to the saddle and 2–homoclinic
orbits to the saddle–focus is shown. And it is also proved that, corresponding to each 1–homoclinic (resp. 2–homoclinic) orbit
Γ, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1–periodic (resp.
2–periodic) and accumulate onto Γ. Moreover, each 2–homoclinic orbit may be also accumulated by a sequence of reversible 4–homoclinic
orbits.
The second author is the corresponding author
Project supported by NNSFC under Grant 10371040 |
| |
| Keywords: | reversible condition homoclinic orbit Poincare map periodic orbit saddle-focus |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
