Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures

M. N. Hounkonnou   ; M. J. Landalidji   ; M. Mitrović

Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 403-423

Résumé

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.

Détail

Keywords: Bi-Hamiltonian structure, noncommutative phase space, recursion operator, Kepler dynamics, dynamical symmetry groups.

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