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• 天元讲堂（7.24）微分方程系列报告
• 浏览量：366 发布人：佚名 发布时间：2017-07-21 11:22:45

• 题目：Some problems in the unique normal form theory

陈国廷 （法国里尔第一大学数学系主任）

时间：7月24日 维格堂113   8：30-9：20

摘要：我们将先介绍唯一正规型理论的一般方法. 然后讨论几个具体的正规型问题:

平面幂零向量场, Hopf-zero向量场，带参数距阵的正规型.

题目：Center of planar quasi-homogeneous polynomial differential systems

于江（教授，上海交通大学）

时间：7月24日 维格堂113   9：30-10：20

摘要：In this paper, we characterize the centers of the quasi-homogeneous but non-homogeneous planar polynomial differential systems of any degree $n\in \mathbb N$. We prove that  systems do not admit centers if $n$ is even, and present the sufficient and necessary conditions that the systems admit a center if $n$ is odd. Furthermore, we provide an algorithm to obtain quasi-homogeneous but non-homogeneous systems with center for a given order. As an example, we characterize the center of the quasi-homogeneous but non-homogeneous of degree $7$.

题目： Versal unfolding of planar systems at degenerate equilibria（I）（II）

唐异垒（副教授，上海交通大学

时间：7月24日 维格堂113  1）；  10：30-11：20；  11：30-12：20

摘要： In this talk we study bifurcations of a planar system  at a degenerate equilibrium, which has a zero linearization. We prove that such a degenerate system is of codimension 3 degeneracy in their classes. So  we introduce unfolding parameters to versally unfold the degenerate systems in the classes.  We display all bifurcations such as pitchfork bifurcation, saddle-center bifurcation and the Bogdanov-Takens bifurcati