| 邓桂丰,刘福窑,路秋英,张伟鹏.一类3维反转系统中的异维环分支[J].数学年刊A辑,2013,34(4):401~414 |
| 一类3维反转系统中的异维环分支 |
| 3-Dimensional Reversible System |
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| DOI： |
| 中文关键词: 异维环, 反转系统, 异宿分支, 活动标架 |
| 英文关键词:Heterodimensional cycle, Reversible system, Heteroclinic bifurca-
tion, Local coordinate moving frame |
| 基金项目:国家自然科学基金 (No.11101283, No.11178014,No.11101370, No.11001041)和上海市教育委员会科研创新基金(No.12YZ173) |
| Author Name | Affiliation | E-mail | | DENG Guifeng | School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China. | maximedgf@163.com | | LIU Fuyao | School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China. | liufuyao@lixin.edu.cn | | LU Qiuying | Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China. | qiuyinglu@163.com | | ZHANG Weipeng | School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China. | zhangwp996@nenu.edu.cn |
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| 中文摘要: |
| 研究了一类3维反转系统中包含2个鞍点的对称异维环分支问题, 且仅限于研究系统的线性对合R的不变集维数为1的情形.
给出了R-对称异宿环与R-对称周期轨线存在和共存的条件, 同时也得到了R-对称的重周期轨线存在性. 其
次, 给出了异宿环、 同宿轨线、 重同宿轨线和单参数族周期轨线的存在性、 唯一性和共存性等结论,
并且发现不可数无穷条周期轨线聚集在某一同宿轨线的小邻域内. 最后给出了相应的分支图. |
| 英文摘要: |
| The authors study the bifurcations of symmetric heterodimensional cycles with
two saddle points in 3-dimensional reversible system when the fixed points space of the linear
involution R is 1-dimensional. Firstly the existence and coexistence of R-symmetric hetero-
clinic loop and R-symmetric periodic orbit are obtained. The double R-symmetric periodic
orbit is also found. Secondly, the authors present sufficient conditions for the existence,
uniqueness and coexistence of heteroclinic loop, homoclinic loops, double homoclinic loop
and a single-parameter family of periodic orbits. It is shown that infinitely many periodic
orbits accumulate along a homoclinic loop. Moreover, the bifurcation surfaces and their
existence regions are located. |
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