中文摘要：

研究Birkhoff系统对称性的摄动与绝热不变量．给出了未受扰Birkhoff系统的Lie对称性导致的Hojman型精确不变量．基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Birkhoff系统Lie对称性的摄动，得到了系统的一类新型绝热不变量．举例说明结果的应用．

英文摘要：

The perturbation of symmetries and adiabatic invariants for Birkhoffian system are studied. The exact invariants in the form of Hojman conserved quantities introduced by the Lie symmetries of Birkhoffian system without perturbations are given. Based on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Birkhoffian system under the action of small disturbance is investigated, and a new type of adiabatic invariants of the system are obtained. An example is given to illustrate the application of the results.