LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS  

作　　者：Zhao Yong Han Maoan Yang Junmin 

机构地区：[1]Institute of Math., Shanghai Normal University, Shanghai 200234

出　　处：《Annals of Differential Equations》2007年第4期593-602,共10页微分方程年刊（英文版）

基　　金：the National Natural Science Foundation of China under Grant (No.10671127);by Shanghai Shuguang Genzong Project(04SGG05)

摘　　要：In this paper, we are concerned with a cubic near-Hamiltonian system, whose unperturbed system is quadratic and has a symmetric homoclinic loop. By using the method developed in [12], we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop. Further, we give a condition under which there exist 4 limit cycles.In this paper, we are concerned with a cubic near-Hamiltonian system, whose unperturbed system is quadratic and has a symmetric homoclinic loop. By using the method developed in [12], we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop. Further, we give a condition under which there exist 4 limit cycles.

关 键 词：limit cycles homoclinic loop near-Hamiltonian systems cubic perturbations Melnikov method 

分 类 号：O17[理学—数学]