Limit cycle bifurcations near double homoclinic and heteroclinic loops of a class of cubic Hamiltonian systems
数学专题报告
报告题目(Title)：Limit cycle bifurcations near double homoclinic and heteroclinic loops of a class of cubic Hamiltonian systems
报告人(Speaker)：熊艳琴教授（南京信息工程大学数学与统计学院）
地点(Place)：腾讯会议：122387930 | 密码：273451
时间(Time)：2026年3月31日（周二）10:00-11:30
邀请人(Inviter)：赵丽琴
报告摘要
This paper studies the double homoclinic and heteroclinic bifurcations by perturbing a cubic Hamiltonian system with polynomial perturbations of degree n. It is proved that 5[(n-1)/2], n ≥ 3 and 2[(n-1)/2] limit cycles can be bifurcated from the period annuli near the double homoclinic loop and the heteroclinic loop, respectively. This result improves the lower bound on the number of the bifurcated limit cycles comparing with the known results for the related problems. To achieve our results, we develop the techniques on calculating the base and the relative relations of the elements in the base, formed partly by curve integral functions along ovals of level sets of the Hamiltonian function, which appear in the expansions of the first order Melnikov functions.
主讲人简介
熊艳琴，南京信息工程大学数学与统计学院，教授，博士研究生导师，从事微分方程与动力系统的研究工作，主要研究极限环的 Hopf 分支、同异宿分支、Poincare 分支；周期函数的临界周期分支；不变环面的存在性及中心焦点问题等，已在SCI期刊杂志（JDE、DCDS、JMAA等）发表 40 余篇论文。担任美国数学会《数学评论》及德国《数学文摘》的评论员，承担两项国家级项目以及多项省级项目。
