自由Birkhoff系统的对称性摄动及其逆问题
The perturbation of symmetries and the inverse problems for freedom Birkhoffian system
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摘要: 研究在小干扰力作用下自由Birkhoff系统的对称性摄动与不变量之间的关系,讨论拓宽绝热不变量的描述范围,研究绝热不变量的结构方程;揭示高阶绝热不变量存在的条件与无穷小对称变换群的摄动之间的正反关系,证明高阶绝热不变量存在的条件及形式,并举例说明结果的应用.Abstract: The relation of the perturbation of symmetries and adiabatitic invariants is studied;the positive and negative relation between the existence conditions of high-order adiabatic invariants and the preturbation of infinitesimal symmetric transformation group is revealed,the existence conditions and forms of high-order adiabatic invariants are proved,and then an example to illustrate the application of the results is given.