一类三次系统q=p=0型奇点的判定量与中心或焦点的判定

Deciding Values of q=p=0 Singular Point and Focus-or-center Judging for A Class of Cubic System

分别求出了一类平面三次系统q=p=0型奇点结构的两种相关判定量的前9个和前6个量,并证明当这些量都为0时后面的量将均为0;然后根据这些判定量具体分析出这类系统原点为中心或焦点的所有可能情形,并给出了应用实例。

Through computing and deducing, first 9 and first 6 quantities of all the singular point deciding values of the q=p=0-origin for a class of cubic system are obtained, it is demonstrated that as these are zero the quantities followed are zero, too. Based on the judgment, the possible situations of focus-or-center of the system are analyzed and example for application is also given.