PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE-LOOP

查看全文 作　　者：ZHAO YULIN,WU XIAOMING,ZHU SIMING Department of Mathematics. Zhongshan University, Guangzhou 510275. China. E-mail: mcszyl@zsu.edu.cn 出　　处：《Chinese Annals of Mathematics,Series B》索引2002年第23卷第1期,共10页 基　　金：the National Natural Science Foundation of China (No.10101031. No. 10071097). Guangdong Natural Science Foundation (No. 001289) 摘　　要：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. 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