Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory

Abstract

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 analyze of the galactic dynamics, or from the motion of the atomic particles in physics.