Abstract
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.
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