四次和五次平面拟齐次多项式系统的首次积分  

The First Integrals of Planar Quartic and Quintic Quasi-homogeneous Polynomial Differential System

作　　者：邱宝华[1] 梁海华[1] 

机构地区：[1]广东技术师范学院计算机科学学院,广东广州510665

出　　处：《广东技术师范学院学报》2015年第11期1-11,共11页Journal of Guangdong Polytechnic Normal University

基　　金：国家自然科学基金(No.11201086);广东省高等学校优秀青年教师培养计划(No.Yq2013107)项目资助

摘　　要：本文研究四次和五次平面多项式不可约的拟齐次微分系统的首次积分.对于四次拟齐次不可约系统,我们根据已有文献给出的标准型计算出所有的首次积分;而对于五次拟齐次不可约系统,我们构造适当的线性变换,结合已有文献的结论,得到系统的标准型,最后计算出其所有首次积分.In this paper, the first integrals of planar quartic and quintic quasi-homogeneous but nonhomogeneous coprime polynomial differential system was investigated. In the quartic quasi-homogeneous coprime polynomial system, the first integrals were computed according to their canonical forms which had been given in literature. For quintic quasi-homogeneous coprime polynomial system, doing a appropriate linear transformation and using the given conclusions about quintic systems, the canonical forms of all quintic systems were obtained. Lastly their first integrals were calculated.

关 键 词：拟齐次 标准型 首次积分 

分 类 号：O172.2[理学—数学]