报告题目：On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order $m$

报告人：熊艳琴教授，南京信息工程大学

报告时间：2024年7月1日（周一）10:00-11:00

报告地点：20-308

报告摘要：In this talk, we investigate the expansions of Melnikov functions near a homoclinic loop with a nilpotent cusp of order $m$. It presents a methodology for calculating all coefficients in these expansions, which can be employed to study the problem of limit cycle bifurcation. As an application, by utilizing the obtained results, the paper rigorously establishes that a polynomial Li\'{e}nard system of degree n+1 has at least n+[n/4] limit cycles near the homoclinic loop with a nilpotent cusp of order one. This work not only updates and generalizes existing results, but also provides a rigorous application of the obtained findings in the context of limit cycle bifurcation.

报告人简介：熊艳琴，南京信息工程大学，数学与统计学院教授，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。