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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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  • https://www.mathnet.ru/eng/tmf10017
  • https://doi.org/10.4213/tmf10017
  • https://www.mathnet.ru/eng/tmf/v207/i3/p403
    • This publication is cited in the following 5 articles:
    1. J. F. Cariñena, H. Figueroa, P. Guha, “A primer on noncommutative classical dynamics on velocity phase space and Souriau formalism”, Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, 2023, 533  crossref
    2. M. N. Hounkonnou, B. H. Degbedji, F. Melong, M. Mitrović, “(Hom−)f-generalized Witt algebras”, Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, 2023, 331  crossref
    3. M. N. Hounkonnou, M. J. Landalidji, M. Mitrovic, “Hamiltonian dynamics of a spaceship in Alcubierre and Gödel metrics: Recursion operators and underlying master symmetries”, Theoret. and Math. Phys., 212:1 (2022), 1001–1018  mathnet  crossref  crossref  mathscinet  adsnasa
    4. F. Wang, Sh. Muhammad, A. Al-Ghamdi, M. Higazy, M. M.A. Khater, “Novel computational technique; the second positive member in a new completely integrable hierarchy”, Journal of Ocean Engineering and Science, 2022  crossref
    5. M. N. Hounkonnou, M. J. Landalidji, M. Mitrović, “Einstein field equation, recursion operators, noether and master symmetries in conformable Poisson manifolds”, Universe, 8:4 (2022), 247  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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