具有退化鞍点的同宿轨附近的Melnikov展开式  

The Melnikov expansion of a homoclinic loop with a degenerate saddle

作　　者：尚德生 陈琛 SHANG Desheng;CHEN Chen(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255049,China;State Grid Zibo Power Supply Company,Shandong Electric Power Corporation,Zibo 255000,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255049 [2]国网山东省电力公司淄博供电公司,山东淄博255000

出　　处：《山东理工大学学报（自然科学版）》2023年第5期38-42,58,共6页Journal of Shandong University of Technology:Natural Science Edition

基　　金：山东省高等教育本科教学改革研究项目(Z2022274)。

摘　　要：对具有退化鞍点的同宿轨附近的一阶Melnikov函数的展开式进行探索,导出了其具体展开式,并对m=n=2时的情形,给出展开式前八项及其系数。In this paper,the expansion of the first order Melnikov function of a homoclinic loop which is connected with a degenerate saddle is studied,and then the general expression of this function is obtained.The first eight coefficients of the expansion of the Melnikov function are given for the case of m=n=2.

关 键 词：退化鞍点 MELNIKOV函数 极限环 同宿轨 分支 

分 类 号：O175.1[理学—数学]