Perturbation to Mei Symmetry and Adiabatic Invariants for Disturbed El-Nabulsi's Fractional Birkhoff System |
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| Authors: | SONG Chuan-Jing ZHANG Yi |
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| Institution: | 1.College of Science, Nanjing University of Science and Technology, Nanjing 210094, China;2.College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China |
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| Abstract: | For El-Nabulsi's fractional Birkhoff system, Mei symmetry perturbation, the corresponding Mei-type adiabatic invariants and Noether-type adiabatic invariants are investigated in this paper. Firstly, based on El-Nabulsi-Birkhoff fractional equations, Mei symmetry and the corresponding Mei conserved quantity, Noether conserved quantity deduced indirectly by Mei symmetry are studied. Secondly, Mei-type exact invariants and Noether-type exact invariants are given on the basis of the definition of adiabatic invatiant. Thirdly, Mei symmetry perturbation, Mei-type adiabatic invariants and Noether-type adiabatic invariants for the disturbed El-Nabulsi's fractional Birkhoff system are studied. Finally, two examples, Hojman-Urrutia problem for Mei-type adiabatic invariants and another for the Noether-type adiabatic invariants, are given to illustrate the application of the results. |
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| Keywords: | Mei symmetry conserved quantity adiabatic invariant El-Nabulsi's fractional Birkhoff system |
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