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中文摘要：
为了揭示小扰动作用下对称性的改变与其不变量之间的内在关系,该文研究了时间尺度上Lagrange系统的Noether对称性摄动与绝热不变量问题。给出了时间尺度上Lagrange系统的运动微分方程、Noether对称性与精确不变量,还给出了绝热不变量的定义,研究了时间尺度上Lagrange系统的绝热不变量。最后举例说明了结果的应用,证明了该文方法及结果的适用性。
英文摘要：
In order to reveal the internal relationships between the symmetry change and the invariant under the small disturbance, the perturbation to the Noether symmetry and adiabatic invariants for Lagrangian systems on time scales are studied in this paper. The differential equations of motion, the Noether symmetry and exact invariant for Lagrangian systems on time scales are presented. The definition of the adiabatic invariant on time scales is given, and the perturbation to the Noether symmetry and adiabatic invariants for Lagrangian systems on time scales are investigated. Finally,an example is given to illustrate the method and results.
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