A new type of adiabatic invariants for Birkhoffian system
Birkhoff系统的一类新型绝热不变量

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.