相对论Birkhoff系统的对称性与稳定性

讨论了相对论Birkhoff系统的三种对称性之间的关系，并利用Liapunov方法得到系统稳定性 的若干判据.随后，应用能量-Casimir函数法将系统稳定性与守恒量联系在了一起，并给出 了算例. 关键词： 相对论Birkhoff系统 对称性关系 稳定性 Liapunov方法 能量-Casimir函数

Symmetry and stability of a relativistic birkhoff system

Relationships among the three symmetries——Noether symmetry,Lie symmetry and M ei symmetry of a relativistic Birkhoff system have been obtained. Some stabilit y criteria are given by using Liapunov method. Finally the conservation quanti ty and the stability of the relativistic Birkhoff system are correlated by the Energy－Casimir functional, and an example is given, to illustrate the applicat ion of the method.