Lie Symmetries, Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System

• Published in: Chinese physics letters Vol. 27; no. 1; pp. 5 - 8
• Main Author: 李彦敏
• Format: Journal Article
• Language: English
• Published: IOP Publishing 2010
• Subjects: Adiabatic flow; Birkhoff系统; Conservation; Differential equations; Invariance; Invariants; Lie对称性; Perturbation; Symmetry; Transformations; 对称性摄动; 微分方程; 无限小变换; 绝热不变量
• ISSN: 0256-307X; 1741-3540
• DOI: 10.1088/0256-307X/27/1/010202

We study the perturbation to symmetries and adiabatic invariants of a generalized Birkhoff system. Based on the invariance of differential equations under infinitesimal transformations, Lie symmetries, laws of conservations, perturbation to the symmetries and adiabatic invariants of the generalized Birkhoff system are presented. First, the concepts of Lie symmetries and higher order adiabatic invariants of the generalized Birkhoff system are proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate the method and results.