| PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE－LOOP |
| |
| 引用本文： | ZHAO Yulin,WU Xiaoming,ZHU Siming. PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE－LOOP[J]. 数学年刊B辑(英文版), 2002, 23(1): 85-94 |
| |
| 作者姓名： | ZHAO Yulin WU Xiaoming ZHU Siming |
| |
| 作者单位： | ZHAO YULIN，WU XIAOMING，ZHU SIMING Department of Mathematics. Zhongshan University，Guangzhou 510275. China. E-mail: mcszyl@zsu.edu.cn |
| |
| 基金项目： | the National Natural Science Foundation of China (No.10101031. No. 10071097). Guangdong Natural Science Foundation (No. 001289) |
| |
| 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…
|
| 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： | 2000-05-06 |
| 修稿时间： | 2000-11-03 |
PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE-LOOP |
| |
| ZHAO Yulin,WU Xiaoming and 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 |
| |
| Authors: | ZHAO Yulin WU Xiaoming ZHU Siming |
| |
| Affiliation: | Department of Mathematics, Zhongshan University, Guangzhou 510275, China |
| |
| 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. |
| |
| Keywords: | Limit cycles Quadratic systems Abelian integrals |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息 |
|
点击此处可从《数学年刊B辑(英文版)》下载免费的PDF全文 |
