| Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium |
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| 作者姓名： | Xingbo LIU Xianlong FU Deming ZHU |
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| 作者单位： | Xingbo LIU Xianlong FU Deming ZHU Department of Mathematics，East China Normal University，Shanghai 200062，China. |
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| 基金项目： | 国家自然科学基金;上海市领先专业学科基金 |
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| 摘 要： | In this paper, the authors develop new global perturbation techniques for detecting the persistence of transversal homoclinic orbits in a more general nondegenerated system with action-angle variable. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in one dimensional manifold, and does not have to be completely integrable or near-integrable. By constructing local coordinate systems near the unperturbed homoclinic orbit, the conditions of existence of transversal homoclinic orbit are obtained, and the existence of periodic orbits bifurcated from homoclinic orbit is also considered.
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| 关 键 词： | 分歧 同宿轨 鞍中心平衡 坐标系统 |
| 收稿时间： | 2 June 2005 |
Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium |
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| Xingbo LIU,Xianlong FU,Deming ZHU.Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium[J].Chinese Annals of Mathematics,Series B,2007,28(1):81-92. |
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| Authors: | Xingbo LIU Xianlong FU and Deming ZHU |
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| Institution: | Department of Mathematics, East China Normal University, Shanghai 200062, China. |
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| Abstract: | In this paper, the authors develop new global perturbation techniques for detecting the persistence of transversal homoclinic orbits in a more general nondegenerated system with action-angle variable. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in one dimensional manifold, and does not have to be completely integrable or near-integrable. By constructing local coordinate systems near the unperturbed homoclinic orbit, the conditions of existence of transversal homoclinic orbit are obtained, and the existence of periodic orbits bifurcated from homoclinic orbit is also considered. |
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| Keywords: | Local coordinate system Homoclinic orbit Bifurcation |
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