| On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z3 Invariant Quintic Perturbations |
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| 引用本文： | Yu Hal WU Mao An HAN. On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z3 Invariant Quintic Perturbations[J]. 数学学报(英文版), 2007, 23(5): 869-878. DOI: 10.1007/s10114-005-0790-3 |
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| 作者姓名： | Yu Hal WU Mao An HAN |
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| 作者单位： | [1]Department of Mathematics, Jiang Su University, Zhenjiang 212013, P. R. China [2]Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China |
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| 基金项目： | The research is supported by fund of Youth of Jiangsu University（05JDG011） |
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| 摘 要： |
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| 关 键 词： | 同宿环 Z3变量五次摄动 哈密尔敦函数 分歧 |
| 收稿时间： | 2004-07-13 |
| 修稿时间： | 2004-07-132004-11-08 |
On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z3 Invariant Quintic Perturbations |
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| Yu Hai Wu,Mao An Han. On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z3 Invariant Quintic Perturbations[J]. Acta Mathematica Sinica(English Series), 2007, 23(5): 869-878. DOI: 10.1007/s10114-005-0790-3 |
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| Authors: | Yu Hai Wu Mao An Han |
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| Affiliation: | (1) Department of Mathematics, Jiang Su University, Zhenjiang 212013, P. R. China;(2) Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China |
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| Abstract: | A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurcation, homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied. It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given. |
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| Keywords: | homoclinic loop bifurcation heteroclinic loop bifurcation Hopf bifurcation stability limit cycles |
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