具有幂零临界点的Linard系统的中心-焦点判定

THE DISCRIMINATION OF CENTER AND FOCUS OF LINARD SYSTEM WITH NILPOTENT CRITICAL POINT

本文研究了一类具有幂零临界点的Linard系统的中心-焦点判定.利用Cherkas方法,得到系统的广义Lyapunov常数,分析了系统奇点稳定性与中心条件,推广了文[6]对于初等临界点中心焦点判定的结果.

The problem of discrimination between center and focus is one of the basic problems in the theory of planar autonomous differential system.In this paper,we study the discrimination of center and focus of Li＇enard system with nilpotent critical point by applying Cherkas method.We obtain the generalized Lyapunov constants,and analysis the stability of singularity and get the condition of center.Therefore the results about discrimination between center and focus of the elementary critical point in[6]are improved.