Abstract
For a relativistic Birkhoffian system, the Lie symmetricalperturbation and adiabatic invariants of generalized Hojmantype are studied under general infinitesimal transformations.On the basis of the invariance of relativistic Birkhoffian equationsunder general infinitesimal transformations, Lie symmetricaltransformations of the system are constructed, which only dependon the Birkhoffian variables. The exact invariants in the formof generalized Hojman conserved quantities led by the Lie symmetriesof relativistic Birkhoffian system without perturbations aregiven. Based on the definition of higher-order adiabatic invariantsof a mechanical system, the perturbation of Lie symmetries forrelativistic Birkhoffian system with the action of small disturbanceis investigated, and a new type of adiabatic invariants of thesystem is obtained. In the end of the paper, an example is givento illustrate the application of the results.
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