三次系统存在一类双纽线分界线环充要条件

A Necessary and Sufficient Condition for the Existence of a Class 0f Double Folium Separatrix Cycles in a Central Symmetrical Cubic System

给出了中心对称三次系统存在一类双纽线分界线环的充要条件，并举出此系统至少还存在四个极限环的（2．2）分布的例子．还举出了中心对称三次系统至少存在六个极限环作（3.3）分布以及五个极限环，其中一个极限环包围作（2．2）分布的四个极限环的例子．

In this Paper, we provide a necessary and sufficient condition for the existence of a class of double folium seperatrix cyeles in a central symmetrical cubic system. And give an example to show that this system can at least exist four limit cycles which distribute in the form of (2. 2). Again we give the example that the central symmetrical cubic system can exist at least six limit eycles which distribute in the form of (3.3) of five limit cyeles,in which four of them distribute in the form (2. 2)and are surrounded by another one.