Perturbation to Lie Symmetry and Generalized Hojman Adiabatic Invariants for Relativistic Hamilton System

Based on the concept of higher-order adiabatic invariants ofmechanical system with action of a small perturbation, the perturbationto Lie symmetry and generalized Hojman adiabatic invariants for the relativisticHamilton system are studied. Perturbation to Lie symmetry is discussed under generalinfinitesimal transformation of groups in which time is variable. The form and thecriterion of generalized Hojman adiabatic invariants for this system are obtained.Finally, an example is given to illustrate the results.