中文摘要：

文章研究了一类五次Lenard系统的细中心与局部临界周期分支问题，利用计算机代数系统Math-ematica进行奇点量与周期常数的计算，导出了系统原点的中心条件和细中心阶数。结果证明：该系统在原点最多能分支5个局部临界周期分支。

英文摘要：

In this paper ,the weak centers of a quintic Lenard system and the local bifurcations of criti-cal periods are investigated .By means of the calculation of singular point values and period constants using the computer algebra system Mathematica ,the center conditions and the orders of weak centers of the origin of the system are obtained .Finally ,it is proved that there are at most five local bifurca-tions of critical periods at the origin of the system .