Melnikov函数在含有两个幂零尖点的双异宿环附近的展开式  

On the expansion of the Melnikov function near a double heteroclinic loop with two nilpotent cusps

作　　者：苗稼乐 杨俊敏 MIAO Jiale;YANG Junmin(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,Hebei,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《上海师范大学学报（自然科学版）》2020年第3期295-310,共16页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The Natural Science Foundation of China(11971145);The Natural Science Foundation of Hebei Province(A2019205133)。

摘　　要：考虑未扰Lienard系统x=y,y=-g(x),其中deg g(x)=7,当该系统分别含有2,3,4和5个奇点时,给出了其所有的不同拓扑类型的相图,并给出了Melnikov函数在含有2个幂零尖点和1个双曲鞍点的双异宿环附近的展开式和得到极限环的条件.In this paper,we give all the different topological types of phase portrait for the unperturbed Lie´nard system x=y,y=−g(x)in the case that deg g(x)=7 and the system has 2,3,4 and 5 singular points,respectively.We then give the expansion of Melnikov function near a double heteroclinic loop with two nilpotent cusps and one hyperbolic saddle.We also give the conditions to obtain the limit cycles.

关 键 词：极限环 LIÉNARD系统 近哈密顿系统 异宿环 MELNIKOV函数 

分 类 号：O193[理学—数学]