含有二阶幂零鞍点的双同宿环附近的极限环分支（英文）  

Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2

作　　者：田焕欢 Tian Huanhuan(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2018年第3期338-348,共11页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The National Natural Science Foundation of China(11771296,11431008,11701375)

摘　　要：研究平面微分系统的极限环个数问题与Hilbert第十六问题的第二部分.考虑一类near-Hamiltonian系统,其未扰系统有一个含有二阶幂零鞍点的双同宿环且在双同宿环附近有三族周期轨.研究了首阶Melnikov函数在双同宿环附近的展开式和展开式的各项系数,得出了此类系统在双同宿环附近可以出现的极限环个数.具体来说,证得此类系统在某些条件下可在双同宿环附近出现11,13,14和16个极限环,并给出了应用实例.Determining the number of limit cycles of a planar differential system is related to the second part of Hilbertls 16th problem. In this paper, a near-Hamiltonian system is studied, where the unper- turbed system has a double homoclinic loop with second order nilpotent saddle and has three families of periodic orbits around the loop. By investigating the expansions of the first order Melnikov functions near the double homoclinic loop as well as their coefficients, the numbers of limit cycles that may appear around the loop are obtained. To be specific, it is shown that there may exist 11, 13, 14 or 16 limit cycles under some conditions. Moreover, an example is given to illustrate the theoretical result.

关 键 词：同宿环 幂零鞍点 极限环 

分 类 号：O175.12[理学—数学]