中文摘要：

讨论一类七次多项式系统原点的中心与等时中心条件的问题。通过复线性变换,把七次实系统转化为复系统,可求出该系统原点的前16个奇点量,从而得到原点成为中心的条件。对系统原点的周期常数进行计算和化简,得到原点成为等时中心的必要条件,并通过时角差定理等方法证明了这些条件也是充分的。由此解决了这类七次系统的中心和等时中心条件。

英文摘要：

The centers and isochronous centers of the origin for a class of seven-degree system were studied.Through a complex transformation,the real systems were transformed into complex ones.After calculating the first sixteen singular point values,we obtained conditions for the origin to be a center.Then necessary conditions for the origin to be an isochronous center was found through computing and simplifying the period constants.Moreover,the sufficiency were proved by methods of time-angle difference and so on.Hence,the centers and isochronous centers conditions for this class of seven-degree system were solved.