拟齐次平面多项式系统的逆积分因子  

Inverse Integrating Factors of Quasi-Homogeneous Planar Polynomial Systems

作　　者：韩美佳[1] 黄土森[1] HAN Meijia HUANGTusen(School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2016年第6期939-944,共6页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：浙江省自然科学基金项目(LY15A010021)

摘　　要：逆积分因子是研究平面多项式系统可积性问题的重要工具。对于拟齐次多项式系统,利用广义Euler定理证明了它一定存在多项式逆积分因子,并给出了具体表达式;对于由两个拟齐次多项式系统的和所定义的多项式系统,给出存在多项式逆积分因子的一个充分条件,并由此给出几类特殊多项式系统的逆积分因子的计算公式。给出的几个多项式逆积分因子计算例子表明这些结论推广了已有成果。The inverse integrating factor is an important tool to study the integrability problem of planar polynomial systems.For a quasi-homogeneous polynomial system,the existence of polynomial inverse integrating factor is proved by using the generalized Euler’s theorem,and the explicit expression is given.For a polynomial system defined by the sum of two quasi-homogeneous polynomial systems,a sufficient condition for the existence of a polynomial inverse integrating factor is given. Then, the computing formulas of inverse integrating factors for several special polynomial systems are given.The computing examples illustrate that the results in this paper generalize the existing conclusions.

关 键 词：拟齐次多项式系统 多项式逆积分因子 拟齐次分解 

分 类 号：O175.14[理学—数学]