Cyclicity in Polynomial Systems via Algebraic Methods

报告题目：Cyclicity in Polynomial Systems via Algebraic Methods

报告人：Brigita Ferčec（研究员博导），University of Maribor

报告时间：2025年9月23日（周二）16:00-18:00

报告地点：明理楼C302

报告人简介：

Brigita Ferčec 是马里博尔大学能源技术学院以及自然科学与数学学院和应用数学与理论物理研究中心的研究员。她于2009年在马里博尔大学获得硕士学位，并于2013年获得博士学位。她的博士生导师是Valery Romanovskij教授，博士论文主题是常微分方程组的定性分析。她的研究领域包括微分方程和动力系统。

报告内容简介：

We investigate the cyclicity of planar polynomial systems, with emphasis on the bifurcation of limit cycles from singular points. Building on computational tools from commutative algebra, we analyze the structure of Bautin ideals and their role in bounding the number of bifurcating cycles. To overcome difficulties arising from non-radical ideals, we employ polynomial subalgebras adapted to the symmetry of time-reversible systems. Our approach further clarifies the relationship between center conditions and cyclicity, and allows us to distinguish the behavior across irreducible components of the center variety.

主办单位：理学院、科学技术发展研究院、人工智能研究院