一类高次多项式微分系统的几何性态  

On the geometric behavior of a class of higher order polynomial differential systems

作　　者：温翔 李慧 李敏[1] 周正新[1] WEN Xiang;LI Hui;LI Min;ZHOU Zhengxin(School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2022年第6期12-17,共6页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(62173292,12171418).

摘　　要：研究了一类平面高次多项式微分系统为中心系统时的结构形式及其首次积分的表达式,并由此判定与其等价的若干非自治微分系统解的几何性态.In this paper,the structure form of a class of higher order polynomial differential systems with the origin as the center is studied,and the expression of its first integral is given.The geometric properties of the solutions of some equivalent nonautonomous differential systems can be determined.

关 键 词：中心问题 高次系统 反射积分 首次积分 

分 类 号：O175.12[理学—数学]