© 2016, Springer Science+Business Media Dordrecht. We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. The Hamiltonian system here studied comes either from the analysis of the galactic dynamics, or from the motion of the atomic particles in physics.
- Averaging theory
- Galactic dynamics
- Periodic orbits
- Perturbed elliptic oscillators