幂零与退化解析系统的中心与焦点的判别问题
The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
摘要：
本文研究了平面解析向量场的中心是线性型中心的极限。证明了所有的幂零中心都是线性型中心的极限，从而证明了寻找线性型中心的Poincaré-Liapunov方法也可以用来寻找幂零中心.此外，我们证明了退化中心，这是极限的线性型中心也是可检测的庞加莱-李雅普诺夫方法。
英文摘要：
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré--Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré--Liapunov method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
