| 黄璇,王丽英,金银来.任意有限维空间中鞍焦点同宿环的稳定性[J].数学年刊A辑,2009,30(4):563~574 |
| 任意有限维空间中鞍焦点同宿环的稳定性 |
| Stability of Homoclinic Loops to Saddle-Focus in Arbitrarily Finite Dimensional Spaces |
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| DOI： |
| 中文关键词: 高维系统 鞍焦点 同宿环 首次回归映射 压缩性 |
| 英文关键词:Higher dimensional system, Saddle-focus, Homoclinic loop, First
recurrent map, Compressibility |
| 基金项目:国家自然科学基金(No.10671069)资助的项目 |
| Author Name | Affiliation | E-mail | | HUANG Xuan | College of Mathematics and Physics, Jinggangshan University, Ji’an 343009,
Jiangxi, China. | huangxuanhx@126.com | | WANG Liying | Department of Foundation, Zhangjiakou Vocational and Technical College,
Zhangjiakou 075000, Hebei, China. | | | JIN Yinlai | Department of Mathematics, Linyi University, Linyi 276005, Shandong, China. | |
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| 中文摘要: |
| 在改造和扩充空间同宿环的部分邻域稳定性定义的基础上,通过建立首次回归映射并考虑其压缩性和扩张性,对任意有限维空M系统连接双曲鞍焦点的同宿环的稳定性质作了深入的研究,包括在不同的主特征值条件下给出了在其管状邻域内稳定集合(流形)和不稳定集合(流形)的存在性及其维数. |
| 英文摘要: |
| By improving and generalizing the stability definition first given and adaptable
to the space homoclinic loop confined in some partial neighborhood, and then establishing
the first recurrent map and studying its compressibility and expansiveness, the stability is
investigated deeply for the homoclinic loop to a hyperbolic saddle-focus in arbitrarily finite
dimensional spaces. The existence and the dimensions of the stable set (manifold) and
unstable set (manifold) in its tubular neighborhood are given under different conditions for
the leading eigenvalues. |
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