Geodesic
Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 403-423

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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. 
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     author = {M. N. Hounkonnou and M. J. Landalidji and M. Mitrovi\'c},
     title = {Noncommutative {Kepler} dynamics: symmetry groups and {bi-Hamiltonian} structures},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {207},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_3_a5/}
}
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M. N. Hounkonnou; M. J. Landalidji; M. Mitrović. Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 403-423. http://geodesic.mathdoc.fr/item/TMF_2021_207_3_a5/