报告题目：Topological properties on isochronous centers of polynomial Hamiltonian differential systems
报告人：董广峰 副教授（邀请人：李时敏）
时间：2021年4月28日15:00-18:00
地点：北二540
报告提纲:In this talk, we study the topological properties on complex polynomial Hamiltonian differential systems of degree n+1 having an isochronous center of Morse type. Firstly, we prove that if on the level curve containing an isochronous center there is only one singular point, then the vanishing cycle associated to this center is a zero homology cycle on the Riemann surface of a generic level curve. This result provides a positive answer to an open question proposed by L. Gavrilov for a very large class of Hamiltonian systems. Secondly, we obtain a necessary condition for isochronicity that the $n+1$-degree part of the Hamiltonian function must have a factor with multipicity no less than (n+1)/2.Thirdly, we show that if the vanishing cycle associated to an isochronous Morse center is a zero homology cycle on the Riemann surface of a generic level curve, then the real Hamiltonian systems do not admit any isochronous center at all when the degree of the Hamiltonian functions is odd. Therefore we consequently prove that a positive answer to L. Gavrilov's question implies the conjecture proposed by X. Jarque and J. Villadelprat is true.
报告人简介:暨南大学数学系副教授、硕士生导师。主要研究兴趣为微分方程的定性理论、解析系统的几何理论等，发表学术论文10余篇；主持国家自然科学基金项目2项，广东省自然科学基金项目1项。
学习及工作经历:
2002.09-2006.07 中国海洋大学数学系 本科
2008.09-2013.07 北京大学 数学科学学院 硕博连读
2013.08-2015.06 中山大学 数学与计算科学学院 博士后
2015.07-至今 暨南大学 数学系