一类七次多项式系统的中心与等时中心条件  

Centers and isochronous centers for a class of seven-degree system

作　　者：许秋瑾[1] 卢景苹[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2010年第2期182-185,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(10961011)

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。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.

关 键 词：奇点量 中心 等时中心 周期常数 

分 类 号：O175.12[理学—数学]