华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 49-55.

• 应用数学与基础数学 • 上一篇    下一篇

Birkhoff\,系统\,Lie\,对称性逆问题的两种提法和解法

龙梓轩1, 张 毅2   

  1. 1. 苏州科技学院~~数理学院, 江苏 215009;
    2. 苏州科技学院~~土木工程学院, 江苏 215011
  • 收稿日期:2011-06-01 修回日期:2011-09-01 出版日期:2012-05-25 发布日期:2012-05-22

Two formulations and solutions of the inverse problems for Lie symmetries in dynamics of a Birkhoffian system

LONG Zi-xuan 1, ZHANG Yi 2   

  1. 1. College of Mathematics and Physics, Suzhou University of Science and Technology, Jiangsu 215009, China; 2. College of Civil Engineering, Suzhou University of
    Science and Technology, Jiangsu 215011, China
  • Received:2011-06-01 Revised:2011-09-01 Online:2012-05-25 Published:2012-05-22

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摘要： 首先, 列写出\,Birkhoff\,系统\,Lie\,对称性的确定方程、结构方程和守恒量; 其次, 给出\,Birkhoff\,系统\,Lie\,对称性逆问题的两种提法和解法. 结果表明：同一\,Birkhoff\,函数(Birkhoff函数组)和第一积分可以对应不 同的\,Birkhoff\,函数组(Birkhoff函数)和不同的\,Lie\,对称性, 也可以对应相同的\,Lie\,对称性和不同的\,Birkhoff\,函数组\,(Birkhoff函数).}

关键词: Birkhoff系统, Lie对称性, 逆问题

Abstract: First, the determining equations, the structure equations and the conserved quantities of Lie symmetries for a Birkhoffian system were given; then two formulations and solutions of the inverse problems of Lie symmetries for the system were presented. The results show that the same Birkhoffian(Birkhoff's functions) and
first integral can correspond to different Birkhoff's functions(Birkhoffian) and different Lie symmetries, and can also correspond to the same Lie symmetry and different Birkhoff's functions(Birkhoffian).

Key words: Birkhoffian system, Lie symmetry, inverse problem

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