| 耿凤杰,朱德明,廉海荣.四维空间中的异维环分支问题[J].数学年刊A辑,2011,32(2):129~140 |
| 四维空间中的异维环分支问题 |
| Bifurcations of Heterodimensional Cycles in R~4 |
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| DOI： |
| 中文关键词: 局部活动坐标架 Poincare映射 异维环 |
| 英文关键词:Local active coordinates Poincare map Heterodimensional cycles |
| 基金项目:国家自然科学基金(No.60974145); 数学天元青年基金(No.10926051); 中央高校基本科研业务费专项资金(No.2010ZY30)资助的项目 |
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| 中文摘要: |
| 利用局部活动坐标架法, 讨论了四维空间中连接两个鞍点的异维环分支问题, 在一些通有的假设下, 分别得到了异维环保存、同宿环、
周期轨存在的充分条件以及保存的异维环与分支出的周期轨共存(或不共存)的结果. |
| 英文摘要: |
| Bifurcations of heterodimensional cycles connecting two saddles in $\mathbb{R}^4$ are studied using local active coordinates.
Under some generic conditions, the authors obtain the persistence of the heterodimensional cycle, existence of one homoclinic loop and one
periodic orbit, coexistence (resp. noncoexistence) of the persistent heterodimensional cycle with the bifurcated periodic orbit. |
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