首次积分在三维幂零向量场规范形化简中的应用  

Further Reduction of Nilpotent Three-dimensional Vector Fields' Normal Form Using First Integral

作　　者：李静[1] 袁星[1] 张丽娜[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《北京工业大学学报》2012年第11期1745-1748,共4页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11072007);北京市自然科学基金资助项目(1122001)

摘　　要：为了研究三维幂零向量场的超规范形(最简规范形、唯一规范形),运用常微分方程与动力系统的规范形理论,利用新次数函数及线性部分的首次积分相结合,获得该系统的一阶规范形;在满足一阶规范形中二次项系数不为零的条件下得到系统的二阶规范形,并证明了其唯一性.To research hypernormal form （ simplest normal form, unique normal form） of nilpotent three- dimensional vector field, the authors obtained the first normal form of this system using normal form theory of ordinary differential equation and dynamical systems, and applying new grading function and the first integral of the linear part. With further reduction the second order normal form was got under the condition that the coefficient of second-degree term was not equal to zero, and its uniqueness was proved.

关 键 词：三维幂零向量场 唯一规范形 首次积分 新次数函数 

分 类 号：O175.1[理学—数学]