| 一类可积非哈密顿系统的极限环个数的上界 |
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| 引用本文： | 张同华,藏红,韩茂安. 一类可积非哈密顿系统的极限环个数的上界[J]. 应用数学, 2004, 17(2): 186-191 |
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| 作者姓名： | 张同华 藏红 韩茂安 |
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| 作者单位： | 1. 上海交通大学数学系,上海,200240
2. 上海交通大学数学系,上海,200240;山东科技大学数学系,山东,泰安,271019 |
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| 摘 要： | In this paper, we consider the perturbations of two non-Hamiltonian integrable systems(1.3)μ, (4.1)μ. For the former,it is proved that the system under the polynomial perturbations hasat most f-n/2] limit cycles in the finite plane and the upper bound is sharp. The proof relies on acareful analysis of a related Abelian integral. For the latter, we obtain an estimate number of isolatedzeros of the corresponding Abelian integral.
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| 关 键 词： | 可积非哈密顿系统 极限环 上界 Abel积分 孤立零点 |
The Upper Bound of the number of Limit Cycles of a Class of Non-Hamiltonian Integrable Systems |
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| ZHANGTong-hua ZANGHong HANMao-an. The Upper Bound of the number of Limit Cycles of a Class of Non-Hamiltonian Integrable Systems[J]. Mathematica Applicata, 2004, 17(2): 186-191 |
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| Authors: | ZHANGTong-hua ZANGHong HANMao-an |
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| Affiliation: | DepartmentofMathematics,ShanghaiJiaotongUniversity,Shanghai200240,China |
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| Abstract: | In this paper, we consider the perturbations of two non-Hamiltonian integrable systems (1.3)μ, (4.1)μ. For the former,it is proved that the system under the polynomial perturbations has at most [n/2] limit cycles in the finite plane and the upper bound is sharp. The proof relies on a ful analysis of a related Abelian integral. For the latter, we obtain an estimate number of isolated zeros of the corresponding Abelian integral. |
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| Keywords: | Limit cycle Abelian integrals Non-Hamiltonian system |
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