Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Birkhoffian Systems

Abstract

This paper investigates the perturbation to Mei symmetry for Birkhoffian systems. The criterion equation of the perturbation to Mei symmetry is established. The condition for existence of generalized Mei adiabatic invariant induced directly from the perturbation to Mei symmetry is obtained, and its form is presented. Finally, an example is discussed to further illustrate the application of the results.

Perturbation to Symmetry and Adiabatic Invariants of General Discrete Holonomic Dynamical Systems

“…Luo [34] gave another new type of adiabatic invariants called the Lutzky adiabatic invariants lately. These studies further inspire interests in research about adiabatic invariants [35][36][37].…”

Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems

“…As a whole, there are three types of perturbations to symmetries: the perturbation to Noether symmetries, [10][11][12] the perturbation to Lie symmetries, [13,14] and the perturbation to Mei symmetries. [15,16] Conformal invariance is built on the scale invariance, the translation invariance, the rotational invariance, and a variety of interactions. [17][18][19][20][21] Perturbation to conformal invariance is a modern approach to find the adiabatic invariants for dynamical systems.…”

Perturbation to Mei Symmetry and Adiabatic Invariants for Disturbed El-Nabulsi's Fractional Birkhoff System*

“…Lately, in 2012, Jiang [32−33] investigated Lie symmetry perturbation and the corresponding Hojman type adiabatic invariants in generalized Hamiltonian systems and generalized Birkhoffian systems, respectively. In 2010, Zhang et al [37] presented the condition and the form for adiabatic invariants of Mei symmetry perturbation in Birkhoffian system. In 2011, Zhang et al [38] studied Mei symmetry perturbation and Mei adiabatic invariants for discrete generalized Birkhoffian system.…”