一类三次多项式微分系统的代数分类及其应用  

Algebraic Classification of a Kind of Cubic Polynomial System and Its Applications

作　　者：刘爱莲[1] 李学敏[2] 朱思铭[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275 [2]山东师范大学数学系,山东济南250014

出　　处：《中山大学学报（自然科学版）》2005年第4期4-8,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10371135)香港中山大学高等学术研究中心基金会资助项目(05M12)

摘　　要：利用Llibre的代数不变式理论,首先由二元二次和二元四次多项式的分类结果,对一次和一次齐次多项式微分系统进行代数分类,同时补充了已有结果中出现的漏洞;其次,由称共变张量审间的性质,对缺二次项的三次微分系统在保证轨线走向不变的前提下进行代数分类,使分类后同类系统的示性多项式有相同零点;最后通过讨沦一类简单系统的有界性说明了分类的方便方处。By Llibre＇s algebraic invariant theory, at first on the basis of classification for quadfic and quatic homogeneous binary polynomial, the plane linear and cubic homogeneous polynomial differential systems are classified. Some deficiency in the references is complemented. Secondly, according to the space of symmetric covariant tensors, on algebraic classification to cubic polynomial differential systems without quadratic terms is obtained, keeping the trajectory direction, which gives the same determinant polynomial for the same class. At last, as an application, the boundedness of a class of cubic systems is disscussed.

关 键 词：代数不变式理论 代数分类 有界性 示性多项式 

分 类 号：O175.12[理学—数学] O175.14[理学—基础数学]