相对论性Birkhoff系统的对称性摄动及其逆问题

研究在小干扰力作用下相对论性Birkhoff系统的对称性摄动问题.建立了相对论性Birkhoff系统的基本原理、运动方程和小扰动方程.讨论该系统的Lie对称性变换和守恒量.研究在无限小变换下该系统的对称性摄动，构造了s阶绝热不变量.给出了绝热不变量存在的条件和形式.研究该系统的对称性摄动逆问题，当系统存在s阶绝热不变量时，得到了该系统的无限小变换的对称性摄动.研究相对论性Birkhoff系统和经典Birkhoff系统对称性摄动之间的关系. 关键词： Lie对称性 摄动 绝热不变量 相对论

Perturbation to the symmetries of relativistic Birkhoffian systems and the inver se problems

In this paper, we have studied the positive problems of perturbation to the symmetries for relativistic Birkhoffian systems under the action of a small force of the disturbance. The fundamental theory, equations of motion and equation of small disturbance of relativistic Birkhoffian systems were established. Lie symmetries and conserved quantity of this systems were given. Perturbation to the symmetries of the systems under infinitesimal transformations, s-order adiabatic invariants, existence conditions and the form of adiabatic invariants were studied. We have also studied the inverse problems of perturbation to the symmetries for relativistic Birkhoffian systems. We obtain the perturbation to the symmetries of the systems under infinitesimal transformations, when the systems possess s-order adiabatic invariants. The relationship between relativistic Birkhoffian systems and classical Birkhoffian systems were studied. Finally an example was presented to illustrate the result.