| Cyclicity of Degenerate Polycycles Through a Saddle-Node and Two Hyperbolic Saddles |
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| 引用本文： | Li Qin ZHAO. Cyclicity of Degenerate Polycycles Through a Saddle-Node and Two Hyperbolic Saddles[J]. 数学学报(英文版), 2005, 21(3): 507-516. DOI: 10.1007/s10114-004-0492-2 |
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| 作者姓名： | Li Qin ZHAO |
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| 作者单位： | Department of Mathematics,Beijing Normal University,Beijing 100875,P.R.China |
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| 基金项目： | Project sponsored by National Science Foundation （19901001） |
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| 摘 要： | This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle （which connects the saddle-node with hp-connection） is equal to 1 and that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp-connection keeps unbroken under the C^∞ perturbations.
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| 关 键 词： | 周期性退化 鞍结点 鞍形双曲线 转换映射 |
| 收稿时间： | 2002-09-18 |
| 修稿时间： | 2002-09-182004-02-09 |
Cyclicity of Degenerate Polycycles Through a Saddle–Node and Two Hyperbolic Saddles |
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| Li Qin Zhao. Cyclicity of Degenerate Polycycles Through a Saddle–Node and Two Hyperbolic Saddles[J]. Acta Mathematica Sinica(English Series), 2005, 21(3): 507-516. DOI: 10.1007/s10114-004-0492-2 |
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| Authors: | Li Qin Zhao |
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| Affiliation: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle–node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle (which connects the saddle–node with hp–connection) is equal to 1 and that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp–connection keeps unbroken under the C∞ perturbations. Project sponsored by National Science Foundation (19901001) |
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| Keywords: | Degenerate polycycle Cyclicity Finitely-smooth normal form Transition map |
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