Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian structures

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, the existence a hierarchy bi-Hamiltonian structures highlighted. Then, family Nijenhuis recursion operators computed discussed.