Perturbation to Lie–Mei Symmetry and Adiabatic Invariants for Birkhoffian Systems

Based on the concept of adiabatic invariant, the perturbation to Lie–Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie–Mei symmetry for the system is presented, and the criterion of the perturbation to Lie–Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.