一类退化中心附近的Melnikov展开式  

The Melnikov expansion near a class of degenerate center

作　　者：尚德生 SHANG Desheng(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255049,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255049

出　　处：《山东理工大学学报（自然科学版）》2023年第6期7-10,19,共5页Journal of Shandong University of Technology:Natural Science Edition

摘　　要：对一类退化中心附近的一阶Melnikov函数的渐进展开式进行探索,分别对m=2,n=1或2时的情形,给出展开式前五项及其系数,并通过一个例子加以说明。In this paper,the expansion of the first order Melnikov near a class of degenerate center is studied,and the general expression of this function is obtained.The first five coefficients of the expansion of the Melnikov are given for the case of m=2,and n=1 or 2.An application example of this method is illustrated.

关 键 词：退化中心 MELNIKOV函数 极限环 分支 

分 类 号：O175.1[理学—数学]