The number of limit cycles from a smooth slow-fast Hopf bifurcation

主讲人：刘长剑  中山大学教授

时间：2021年11月23日10：00

地点：腾讯会议 163 529 004

主办单位：数理学院

主讲人介绍：刘长剑，中山大学数学学院（珠海）教授，北京大学和法国里尔大学联合培养获博士，主要从事常微分定性理论的研究工作，在 Nonlinearity、 J. Diff.  Equa.、 Dis. Cont. Dyn. Sys.等杂志上发表过多篇论文并主持过多项国家基金委项目。

内容介绍：Dumortier and Roussarie proposed a conjecture in their paper (2009, Discrete  Con. Dyn. Sys., 2, 723-781): For any positive integer q, q Abelian integrals  over some non-algebraic curve, form a strict Chebyshev system. If this  conjecture holds, then one can obtain the precise upper bound of the number of  limit cycles that appear near a slow-fast Hopf point. In this talk we develop a  method to estimate the number of zeros of Abelian integrals and prove this  conjecture. This is a joint work with Prof. Chengzhi Li.