| 一类3维反转系统中的异维环分支 |
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| 引用本文： | 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(中文版),2013,34(4):401-414. |
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| 作者姓名： | 邓桂丰 刘福窑 路秋英 张伟鹏 |
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| 作者单位： | 上海立信会计学院数学与信息学院, 上海201620.;上海立信会计学院数学与信息学院, 上海201620.;浙江理工大学数学系, 杭州310018.;东北师范大学数学与统计学院, 长春130024 |
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| 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) |
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| 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.
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| 关 键 词： | 异维环 反转系统 异宿分支 活动标架 |
3-Dimensional Reversible System |
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| DENG Guifeng,LIU Fuyao,LU Qiuying and ZHANG Weipeng.3-Dimensional Reversible System[J].Chinese Annals of Mathematics,2013,34(4):401-414. |
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| Authors: | DENG Guifeng LIU Fuyao LU Qiuying and ZHANG Weipeng |
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| Institution: | School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China.;School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China.;Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China.;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China. |
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| Abstract: | 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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| Keywords: | Heterodimensional cycle Reversible system Heteroclinic bifurca-
tion Local coordinate moving frame |
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