College of Physics Science and Technology, China University
of Petroleum, Dongying 257061, China; Department of Physics and Electronics Science,
Binzhou
University, Binzhou 256603, China; Dezhou University, Dezhou 253023, China
Abstract:
The perturbation to Lie symmetry and another type of Hojman
adiabatic invariants induced from the perturbation to Lie symmetry
for Birkhoffian systems are studied. The exact invariants of Lie
symmetry for the system without perturbation are given. Based on the
concept of adiabatic invariant, the perturbation to Lie symmetry is
discussed and another new type of Hojman adiabatic invariants that
have the different form from that in {\em Acta Phys. Sin.} {\bf 55}
3833] for the perturbed system are obtained.