离散Kepler系统的共形不变性与守恒量

摘要

研究了离散Kepler系统的Lie对称性共形不变性和Noether守恒量,得到了Kepler系统的差分方程和能量演化方程,给出系统的共形不变性定义和共形因子,得到系统的共形不变性是Lie对称性的充要条件.讨论离散Kepler系统的Lie对称性和共形不变性之间的关系,给出系统的离散Noether定理,利用离散变分算法模拟系统的守恒量.%The conformal invariance of the Lie symmetry and the Noether conserved quantities were inves-tigated for discrete Kepler systems.The difference equations and the energy equations of the Kepler sys-tems were obtained.The conformal invariance of the Lie symmetry and the conformal factor were defined for the systems.The necessary and sufficient conditions of the Lie symmetries being the conformal symme-tries were proposed.The relations between the Lie symmetries and the conformal invariance were dis-cussed.The Noether theorems of the systems were derived.An example was given to illustrate the appli-cation of the results.