一类退化尖点环附近Melnikov函数展开式  

The Melnikov expansion of a homoclinic loop with a degenerate cusp

作　　者：尚德生 王政 SHANG Desheng;WANG Zheng(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）》2022年第5期50-55,共6页Journal of Shandong University of Technology:Natural Science Edition

摘　　要：对一类具有退化尖点的同宿轨附近的一阶Melnikov函数展开式,导出了函数M(h,δ)展开式的基本表达形式,对m=1时的情形,给出展开到前八项的表达形式和各项系数。In this paper,the expansion of the first order Melnikov function of a homoclinic loop which is connected with a degenerate cusp is studied,and then we obtain the general expression of the function M(h,δ).Later,the first eight coefficients of the expansion of the Melnikov function are given for the case of m=1.

关 键 词：退化尖点 MELNIKOV函数 极限环 同宿轨 分支 

分 类 号：O175.1[理学—数学]