Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics

下载PDF

导出

摘要 In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located. In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.

作者 XU Yan-cong GENG Feng-jie

机构地区 Department of Mathematics School of Science

出处《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第1期108-118,共11页 高校应用数学学报（英文版）（B辑）

基金 Supported by Science Research Foundation of the Returned Overseas Chinese Scholar,SEM,the NSF of China(11202192) Zhejiang Province(LY13A010020)and Program for Excellent Young Teachers in HNU(HNUEYT2013)

关键词 Bifurcations Homoclinic bellows Periodic orbit Invariant-curve sequences Bifurcations,Homoclinic bellows,Periodic orbit,Invariant-curve sequences

分类号 O186.11 [理学—基础数学]

引文网络
相关文献

参考文献2

1韩茂安,陈健.On the number of limit cycles in double homoclinic bifurcations[J].Science China Mathematics,2000,43(9):914-928. 被引量：16
2Zhu Deming Department of Mathematics, East China Normal University. Shanghai 200062. China.Problems in Homoclinic Bifurcation with Higher Dimensions[J].Acta Mathematica Sinica,English Series,1998,14(3):341-352. 被引量：31

二级参考文献1

1HAN MAOAN.BIFURCATIONS OF LIMIT CYCLES FROM A HETEROCLINIC CYCLE OF HAMILTONIAN SYSTEMS[J].Chinese Annals of Mathematics,Series B,1998,19(2):189-196. 被引量：2

共引文献43

1尚德生,张同华.BIFURCATIONS OF A CUBIC SYSTEM PERTURBED BY DEGREE FIVE[J].Acta Mathematica Scientia,2009,29(1):11-24. 被引量：1
2SHUI Shuliang & ZHU Deming College of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, China,Department of Mathematics, East China Normal University, Shanghai 200062, China.Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips[J].Science China Mathematics,2005,48(2):248-260. 被引量：10
3金银来,朱德明.Bifurcations of rough heteroclinic loop with two saddle points[J].Science China Mathematics,2003,46(4):459-468. 被引量：8
4Wang Yanqin (Dept.of Inform.Sci.,Jiangsu Polytechnic University,Changzhou 213164,Jiangsu) Zhu Deming (Dept.of Math.,East China Normal University,Shanghai 200062).RESONANT BIFURCATIONS OF THE HOMOCLINIC MANIFOLD FOR FOURTH-DIMENSIONAL SYSTEM[J].Annals of Differential Equations,2008,24(1):52-64.
5Yun Tian, Yepeng Xing (Dept. of Math., Shanghai Normal University, Shanghai 200234).ON THE NUMBER OF LIMIT CYCLES OF A CUBIC SYSTEM NEAR A CUSPIDAL LOOP[J].Annals of Differential Equations,2010,26(2):222-226.
6XU YanCong,ZHU DeMing,DENG GuiFeng.Codimension 2 reversible heteroclinic bifurcations with inclination flips[J].Science China Mathematics,2009,52(8):1801-1814.
7金银来,朱德明.高维同宿环扭曲分支与稳定性[J].应用数学和力学,2004,25(10):1076-1082.
8刘兴波,朱德明.伴随超临界分支的通有同宿轨道分支[J].数学学报（中文版）,2004,47(5):957-964.
9HANMAOAN,BIPING.BIFURCATION OF LIMIT CYCLES FROM A DOUBLE HOMOCLINIC LOOP WITH A ROUGH SADDLE[J].Chinese Annals of Mathematics,Series B,2004,25(2):233-242. 被引量：3
10金银来,朱德明.三点粗异宿环分支[J].数学学报（中文版）,2004,47(6):1237-1242.

1Arthur.G.Werschulz.THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM[J].Analysis in Theory and Applications,1998,14(1):1-7. 被引量：1
2傅新楚,周焕文.CHAOTIC BEHAVIOUR OF THE GENERAL SYMBOLIC DYNAMICS[J].Applied Mathematics and Mechanics(English Edition),1992,13(2):117-123.
3YANG LihuaDepartment of Scientific Computing and Computer Applications, School of Mathematics and Computing Science, Zhongshan (Sun Yatsen) University, Guangzhou 510275, China,Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China.Orthogonality in Banach spaces and orthogonal multiscale L^1-approximation[J].Chinese Science Bulletin,1999,44(1):25-35.
4Charles K. Chui (1) , Xianliang Shi (1).SHIFT-INVARIANT BI-INNER PRODUCT FUNCTIONALS ARE INNER PRODUCTS[J].Analysis in Theory and Applications,1999,15(1):103-110. 被引量：10
5薛婷,杨学友,吴斌,叶声华.自由曲面数字化测量中黏性目标识别技术研究[J].光电子．激光,2004,15(12):1488-1491. 被引量：2
6J.Peters,M.Sitharam.ON STABILITY OF m-VARIATE C^1 INTERPOLATION[J].Analysis in Theory and Applications,1993,9(1):18-32.
7薛明志,朱秀阁,田继善.The Properties of Finitely Generated Shift-invariant Subspace in L_(2π)~2[J].Chinese Quarterly Journal of Mathematics,1999,14(2):69-75.
8Deng Feng LI,Tao QIAN.Sufficient Conditions for Shift-Invariant Systems to be Frames in L^2(R^n)[J].Acta Mathematica Sinica,English Series,2013,29(8):1629-1636.
95毫秒值多少钱[J].科技新时代,2011(6):29-30.
10Han Bin Institute of Mathematics Academia Sinica Beijing,100080 China.Some Applications of Projection Operators in Wavelets[J].Acta Mathematica Sinica,English Series,1995,11(1):105-112. 被引量：5

Applied Mathematics(A Journal of Chinese Universities)

2014年第1期

浏览历史

内容加载中请稍等...

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics

参考文献2

二级参考文献1

共引文献43

相关作者

相关机构

相关主题

浏览历史