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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 3, Pages 403–423
DOI: https://doi.org/10.4213/tmf10017 (Mi tmf10017) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures

M. N. Hounkonnoua, M. J. Landalidjia, M. Mitrovićb

a University of Abomey-Calavi, Cotonou, Republic of Benin
b Faculty of Mechanical Engineering, Department of Mathematics and Informatics, University of Niš, Serbia
Full-text PDF (558 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf10017
Abstract: Integrals of motion are constructed from noncommutative (NC) Kepler dynamics, generating $SO(3)$, $SO(4)$, and $SO(1,3)$ 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.
Keywords: Bi-Hamiltonian structure, noncommutative phase space, recursion operator, Kepler dynamics, dynamical symmetry groups.
Funding agency Grant number
International Chair in Mathematical Physics and Applications (ICMPA). UNESCO
Daniel Iagolnitzer Foundation
University of Niš
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.”
Received: 03.12.2020
Revised: 03.12.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 3, Pages 751–769
DOI: https://doi.org/10.1134/S0040577921060064
Bibliographic databases:
Document Type: Article
MSC: 37C10; 37J35; 37K05; 37K10
Language: Russian
Citation: M. N. Hounkonnou, M. J. Landalidji, M. Mitrović, “Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures”, TMF, 207:3 (2021), 403–423; Theoret. and Math. Phys., 207:3 (2021), 751–769
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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