Perturbation to Noether–Lie Symmetry and Adiabatic Invariants for Mechanical Systems in Phase Space

Abstract

Based on the concept of adiabatic invariant, the perturbation to Noether–Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied. The criterion of the Noether–Lie symmetry for the perturbed system is given, and the definition of the perturbation to Noether–Lie symmetry for the system under the action of small disturbance is presented. Meanwhile, the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained.