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Noether's theorems for nonshifted dynamic systems on time scales

Author

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  • Song, Chuan-Jing
  • Cheng, Yao

Abstract

Conserved quantities on time scales for the nonshifted Birkhoffian system and the nonshifted Hamiltonian system are investigated. Firstly, nonshifted Birkhoff equation and nonshifted Hamilton equation on time scales are obtained. Secondly, Noether identities and Noether theorems for the nonshifted Birkhoffian system and the nonshifted Hamiltonian system are achieved. Thirdly, special cases such as the classical Birkhoffian system, the discrete Birkhoffian system, the classical Hamiltonian system, the discrete Hamiltonian system and the nonshifted Lagrangian system are discussed.

Suggested Citation

  • Song, Chuan-Jing & Cheng, Yao, 2020. "Noether's theorems for nonshifted dynamic systems on time scales," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300320300552
    DOI: 10.1016/j.amc.2020.125086
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    References listed on IDEAS

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    1. Agnieszka B. Malinowska & Natália Martins, 2013. "The Second Noether Theorem on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, December.
    2. Song, Chuan-Jing & Zhang, Yi, 2017. "Conserved quantities for Hamiltonian systems on time scales," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 24-36.
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    Cited by:

    1. Zhang, Yi & Jia, Yun-Die, 2023. "Generalization of Mei symmetry approach to fractional Birkhoffian mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Tian, Xue & Zhang, Yi, 2021. "Fractional time-scales Noether theorem with Caputo Δ derivatives for Hamiltonian systems," Applied Mathematics and Computation, Elsevier, vol. 393(C).

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