| 一类可积非哈密顿系统的极限环数目的上界 |
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| 引用本文： | 赵育林,陈海波.一类可积非哈密顿系统的极限环数目的上界[J].大学数学,2008,24(5). |
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| 作者姓名： | 赵育林 陈海波 |
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| 作者单位： | 1. 中南大学,数学学院,湖南,长沙,410075;湖南工业大学,数学系,湖南,株洲,412007
2. 中南大学,数学学院,湖南,长沙,410075 |
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| 摘 要： | 研究了一类可积非哈密顿系统的极限环的上界,利用Abel积分证明其在一类2n+1次多项式扰动下至多可以产生n+1个极限环,并且是可以实现的.
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| 关 键 词： | Mel’nikov函数 non-Hamilton系统 极限环 |
The Upper Bound of the Number of Limit Cycles for a Class of Non-Hamiltonian Integral Systems |
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| ZHAO Yu-lin,CHEN Hai-bo.The Upper Bound of the Number of Limit Cycles for a Class of Non-Hamiltonian Integral Systems[J].College Mathematics,2008,24(5). |
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| Authors: | ZHAO Yu-lin CHEN Hai-bo |
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| Abstract: | We make researches on the upper bound of the number of limit cycles of a class of non-Hamiltonian integral system. Relying on Abelian integral, we prove that the system under the 2n+1 orders polynomial perturbations has at most n+1 limit cycles in the finite plane and the upper bound is sharp. |
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| Keywords: | non-Hamiltonian system Mel’nikov functions limit cycle |
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