Perturbed conformal invariance and Mei adiabatic invariants of the generalized perturbed Hamiltonian systems with additional terms

Abstract This study investigates the relationship between perturbed conformal invariance and Mei symmetry in the generalized perturbed Hamiltonian systems with additional terms. A necessary and sufficient condition is derived to determine whether perturbed conformal invariance can be considered an approximate Mei symmetry. Furthermore, the Mei adiabatic invariants are also obtained. Lastly, an example is presented to demonstrate the key findings.