1∶-2共振系统高次奇点的广义奇点量与可积性  

Generalized Singular Point Quantity and Integrability of the Degenerate Resonant Singular Point of 1∶-2 Resonant System

作　　者：李慧丽[1] 黄文韬[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：《广西科学院学报》2011年第3期182-183,192,共3页Journal of Guangxi Academy of Sciences

摘　　要：利用同胚变换,把p∶-q共振系统的高次奇点化为初等奇点,通过研究初等奇点的性质来研究高次奇点的性质,并运用计算机代数系统求出初等奇点的前20个奇点量,从而得到1∶-2系统在原点邻域可积的必要条件,并证明这些条件的充分性.In this article,integrability of the degenerate resonant singular point of a p∶-q resonant system are studied.Firstly,by means of a homeomorphous transformation,the degenerate resonant singular point of the p∶-q resonant system is transformed into the elementary singular point.Hence the problem is transformed into the study of elementary singular point.The top 20 singular point values are given by using Compute Algebra Mathematica.Then the necessary conditions for the integrability are worked out.At last,the sufficiency of these conditions is proved.

关 键 词：共振系统 高次奇点 奇点量 可积性 

分 类 号：O175.5[理学—数学]