具有共振特征值的轨道翻转双同宿环分支

张天四; 朱德明

具有共振特征值的轨道翻转双同宿环分支

张天四¹,
朱德明²

1.
上海理工大学理学院,上海 200093;2.华东师范大学数学系,上海 200062

基金项目: 国家自然科学基金资助项目(10371040)

详细信息

作者简介:
朱德明(1947- ),男,教授,博士生导师(联系人.E-mail:dmzhu@math.ecnu.edu.cn).

中图分类号: O175.12
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- 被引次数: 0
出版历程
- 收稿日期: 2006-08-29
- 修回日期: 2007-08-06
- 刊出日期: 2007-11-15

Bifurcations of Double Homoclinic Flip Orbits With Resonant Eigenvalues

ZHANG Tian-si¹,
ZHU De-ming²

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;

摘要

摘要: 该文研究了具有轨道翻转的双同宿环四维系统，在主特征值共振和沿轨道奇点处切方向共振下的两种分支．我们分别在系统奇点小邻域内利用规范型的解构造一个奇异映射，再在双同宿环的管状邻域内引起局部活动坐标架，利用系统线性变分方程的解定义了一个正则映射，通过复合两个映射而得到分支研究中一类重要的Poincaré映射，经过简单的计算最终得到后继函数的精确表达式．对分支方程细致地研究，我们给出了原双同宿环的保存性条件，并证明了“大” 1-同宿环分支曲面，2-重“大”1-周期轨分支曲面，“大”2-同宿环分支曲面的存在性、存在区域和近似表达式，及其分支出的“大”周期轨和“大”同宿轨的存在性区域和数量．
- 双同宿轨 /
- 轨道翻转 /
- 周期轨 /
- 共振
Abstract: Concerns double homoclinic loops with or bitflips and two resonant eigenvalues in a fourdimensional system. We use the solution of a normal form system to construct a singular map in some neighborhood of the equilibrium, and the solution of a linear variational system to construct a regular map in some neighborhood of the double homoclinic loops, then compose them to get the important Poincar map. A simple calculation gives explicitly an expression of the associated successor function. By a delicate analysis of the bifurcation equation, we obtain the condition that the original double homoclinic loops are kept, and prove the existence and the existence regions of the large 1-homo clinic orbit bifurcation surface, 2-fold large 1-periodic or bit bifurcation surface, large 2-homoclinic or bit bifur cation surface and their appro ximate expressions. We also locate the large periodic orbits and large homoclinic orbits and their number.
- double homoclinic orbit /
- orbit flip /
- periodic orbit /
- resonance

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参考文献(13)

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