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Lie Symmetries, Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System |
| LI Yan-Min |
| Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000 |
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LI Yan-Min 2010 Chin. Phys. Lett. 27 010202 |
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Abstract 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.
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02.20.Sv
11.30.-j
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Received: 22 October 2009
Published: 30 December 2009
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| PACS: |
02.20.Sv
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(Lie algebras of Lie groups)
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11.30.-j
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(Symmetry and conservation laws)
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