Mahougnon Justin Landalidji
Kepler problem in the harmonic oscillator setting: recursion operator and relevant properties
We study the Hamiltonian dynamics for the Kepler problem perturbed by a harmonic oscillator in parabolic coordinates. We derive the Hamiltonian vector fields describing the system evolution, and
construct associated recursion operator generating the constants of motion. We then infer the existence of a
bi-Hamiltonian structure, introduce master symmetries, and compute a family of conserved quantities.
