| 二阶Birkhoff自治系统的奇点、闭轨、稳定流形与不稳定流形 |
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| 引用本文： | 陈向炜,梅凤翔.二阶Birkhoff自治系统的奇点、闭轨、稳定流形与不稳定流形[J].北京理工大学学报(英文版),1998,7(4):330-336. |
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| 作者姓名： | 陈向炜 梅凤翔 |
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| 作者单位： | 北京理工大学应用力学系!北京，100081 |
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| 基金项目： | 国家自然科学基金;高等学校博士学科点专项科研基金 |
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| 摘 要： | 目的研究二阶Birkhoff自治系统的奇点、闭轨、稳定流形与不稳定流形，方法用常1微分方程的定性方法进行研究，结果与结论给出二阶Birkhoff自治系统的奇点判据、闭轨判据、双曲平衡点判据，得到与其相关的平衡稳定性、稳定流形与不稳定流形等。
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| 关 键 词： | Birkhoff系统 奇点 闭轨 稳定流形 不稳定流形 |
Singular Points, Closed Orbits, Stable Manifolds and Unstable Manifolds of Second Order Autonomous Birkhoff Systems |
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| Chen Xiangwei and Mei Fengxiang.Singular Points, Closed Orbits, Stable Manifolds and Unstable Manifolds of Second Order Autonomous Birkhoff Systems[J].Journal of Beijing Institute of Technology,1998,7(4):330-336. |
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| Authors: | Chen Xiangwei and Mei Fengxiang |
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| Affiliation: | Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081;Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081 |
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| Abstract: | Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained. |
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| Keywords: | Birkhoff system singular point closed orbit stable manifold unstable manifold |
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