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Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian structures

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Abstract

Integrals of motion are constructed from noncommutative (NC ) Kepler dynamics, generating \(\mathrm{SO}(3)\), \(\mathrm{SO}(4)\), and \(\mathrm{SO}(1,3)\) dynamical symmetry groups. The Hamiltonian vector field is derived in action–angle coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family of Nijenhuis recursion operators is computed and discussed.

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Funding

The ICMPA-UNESCO Chair is in partnership with the Association pour la Promotion Scientifique de l’Afrique (APSA), France, and Daniel Iagolnitzer Foundation (DIF), France, supporting the development of mathematical physics in Africa. M. M. is supported by the Faculty of Mechanical Engineering, University of Niš, Serbia, Grant “Research and development of new generation machine systems in the function of the technological development of Serbia.”

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Authors and Affiliations

  1. University of Abomey-Calavi, Cotonou, Republic of Benin

    M. N. Hounkonnou & M. J. Landalidji

  2. Faculty of Mechanical Engineering, Department of Mathematics and Informatics, University of Niš, Niš, Serbia

    M. Mitrović

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  1. M. N. Hounkonnou
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  2. M. J. Landalidji
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  3. M. Mitrović
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Correspondence to M. N. Hounkonnou.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 403-423 https://doi.org/10.4213/tmf10017.

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Hounkonnou, M.N., Landalidji, M.J. & Mitrović, M. Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian structures. Theor Math Phys 207, 751–769 (2021). https://doi.org/10.1134/S0040577921060064

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