拟齐次系统的约化与约化Kowalevskaya指数  

Reduction of Quasi-Homogeneous Autonomous Systems and Reduced Kowalevskaya Exponent

作　　者：刘明惠[1] 管克英[1] 

机构地区：[1]北京交通大学理学院数学系,北京100044

出　　处：《应用数学学报》2008年第4期729-743,共15页Acta Mathematicae Applicatae Sinica

摘　　要：用所接受的单参数李群的特征定义拟齐次自治系统,并且对拟齐次系统进行约化,定义约化系统的约化Kowalevskaya指数,给出该指数与原拟齐次系统的Kawalevskaya指数之间的关系,对二维的拟齐次多项式系统,具体给出约化Kowalevskaya指数特征与拟齐次多项式首次积分的更深入关系.基于约化系统,证明拟齐次系统一般均存在局部的拟齐次首次积分组.A reduction is given for some autonomous systems according to the character of the generator of a Lie group admitted by the systems, and the reduced Kowalevskaya exponents is defined for the the reduced systems, and the relation between the reduced Kowalevskaya exponents and the Kowalevskaya exponents of the original quasi-homogeneity autonomous systems is given. For the two dimensional quasi-homogeneous polynomial system, a more intrinsic relation between the new exponents for the reduced system, the existence and the properties of the homogeneous polynomial first integral is shown. Based on the reduced systems, it is proved that the local homogeneous frst integral system exists in general.

关 键 词：单参数Lie群 拟齐次自治系统 Kowalevskaya指数 首次积分 

分 类 号：O175.14[理学—数学]