| PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE－LOOP |
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| 作者姓名： | ZHAO Yulin WU Xiaoming ZHU Siming |
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| 作者单位： | ZHAO YULIN，WU XIAOMING，ZHU SIMING Department of Mathematics. Zhongshan University，Guangzhou 510275. China. E-mail: mcszyl@zsu.edu.cn |
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| 基金项目： | the National Natural Science Foundation of China (No.10101031. No. 10071097). Guangdong Natural Science Foundation (No. 001289) |
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| 摘 要： | 61. IntroductionConsidcr a Hamiltonian system with smaIl perturbations{::leq:jix:<,\:>!>, (1l.)where X(x, y, e) and Y(I, y, ') are polynomia1s of T, y with coefficients depending analyti-cally on the small paramcter e, and the unperturbed s)ystern (1.l)() has at least onc cel1tersurrounded b}' the compact component r}, of algebraic curveH(x, g) = h, deg H(x, y) = m + 1, nlax{deg X(x. y, '). dog y(J. y. ')} = 7n.Tbe number of ]jm jt cyc]es of (1.1 ). whjcb emergp fIon) Th is equa] to tbe l1…
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| 关 键 词： | 摄动 退化Hamilton系统 鞍点圈 偏微分方程 Abel积分 极限圈 Picard－Fuchs方程 单调性 |
| 收稿时间： | 5/6/2000 12:00:00 AM |
| 修稿时间： | 2000/11/3 0:00:00 |
PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE-LOOP |
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| ZHAO Yulin,WU Xiaoming,ZHU Siming.PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE-LOOP[J].Chinese Annals of Mathematics,Series B,2002,23(1):85-94. |
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| Authors: | ZHAO Yulin WU Xiaoming and ZHU Siming |
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| Institution: | Department of Mathematics, Zhongshan University, Guangzhou 510275, China |
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| Abstract: | The authors investigate a kind of degenerate quadratic Hamiltonian systems with saddle-loop. Under quadratic perturbations, it is proved that the perturbed system has at most two limit cycles in the finite plane. The proof relies on a careful analysis of a related Abelian integral. |
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| Keywords: | Limit cycles Quadratic systems Abelian integrals |
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