| 三维系统中一族闭轨在周期扰动下的分支 |
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| 引用本文： | 刘宣亮,孟笑莹.三维系统中一族闭轨在周期扰动下的分支[J].系统科学与数学,2009,29(8):1034-1043. |
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| 作者姓名： | 刘宣亮 孟笑莹 |
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| 作者单位： | 华南理工大学数学系,广州,510640 |
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| 基金项目： | 国家自然科学基金(10871074) 资助项目 |
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| 摘 要： | 讨论一类三维系统在周期扰动下的分支问题.假设此三维系统有一族闭轨,利用 Poincar\'e映射及积分流形定理,得到了在周期扰动下由这族闭轨产生次调和解和不变环面的条件,并讨论了次调和解的鞍结点分支.
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| 关 键 词： | 分支 次调和解 不变环面. |
| 收稿时间： | 2008-5-19 |
| 修稿时间： | 2008-11-13 |
BIFURCATION OF A THREE-DIMENSIONAL SYSTEM WITH PERIODIC PERTURBATION |
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| LIU Xuanliang,MENG Xiaoying.BIFURCATION OF A THREE-DIMENSIONAL SYSTEM WITH PERIODIC PERTURBATION[J].Journal of Systems Science and Mathematical Sciences,2009,29(8):1034-1043. |
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| Authors: | LIU Xuanliang MENG Xiaoying |
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| Institution: | Department of Mathematics, South China University of Technology, Guangzhou 510640 |
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| Abstract: | In this paper, bifurcation of subharmonic solutions and invariant tori of a three-dimensional system under periodic perturbation is studied. Assume that the unperturbed three dimensional system has a family of closed orbits, by usingPoincar\'e map and integral manifold theory, sufficient conditions for the existence of subharmonic solutions and invariant tori of the perturbed system are obtained. Moreover, saddle-node bifurcation of subharmonic solutions are studied. |
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| Keywords: | Bifurcation subharmonic solutions invariant tori |
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