报告时间：2025年11月27日 15：00-16：00

报 告 人：熊艳琴教授（南京信息工程大学）

报告地点：腾讯会议 191-707-119

报告题目：Limit cycle bifurcations near double homoclinic and heteroclinic loops of a class of cubic Hamiltonian system

内容摘要：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 $5[\frac{n-1}{2}],~n\geq3$ and $2[\frac{n-1}{2}]$ limit cycles can be bifurcated from the period annuli near the double homoclicic 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，数学与统计注册送彩金 教授，江苏省科协青年托举人才，主要从事微分方程与动力系统的研究工作。主持国家自然科学基金项目2项，江苏省自然科学基金3项；被《美国数学会》及德国《数学文摘》聘为特约评论员；已在SCI期刊杂志发表一作论文30余篇，荣获第六届全国青年微分方程暨秦元勋诞辰100周年学术会议优秀论文奖。