| CODIMENSION 3 BIFURCATIONS OFHOMOCLINIC ORBITS WITH ORBITFLIPS AND INCLINATION FLIPS |
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| 作者姓名： | SHUI Shuliang ZHU Deming |
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| 作者单位： | SHUI SHULIANG ZHU DEMING College of Mathematics and Physics，Zhejiang Normal University，Jinhua 321004，Zhejiang，China. Department of Mathematics，East China Normal University，Shanghai 200062，China. |
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| 基金项目： | 华东师范大学校科研和教改项目 |
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| 摘 要： | The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is non-principal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.
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| 关 键 词： | 分支 同宿轨 倾角 周期轨道 数理方程 |
| 收稿时间： | 1/3/2009 12:00:00 AM |
CODIMENSION 3 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS |
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| SHUI Shuliang,ZHU Deming.CODIMENSION 3 BIFURCATIONS OFHOMOCLINIC ORBITS WITH ORBITFLIPS AND INCLINATION FLIPS[J].Chinese Annals of Mathematics,Series B,2004,25(4):555-566. |
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| Authors: | SHUI Shuliang and ZHU Deming |
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| Institution: | 1. College of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
2. Department of Mathematics, East China Normal University, Shanghai 200062, China |
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| Abstract: | The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is non-principal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained. |
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| Keywords: | Bifurcation Homoclinic orbit Orbit flip Inclination flip Periodic orbit |
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