We apply the averaging theory to study a generalized Yang-Mills Hamiltonian system in dimension 6 with six parameters. We provide sufficient conditions on the six parameters of the system which guarantee the existence of continuous families of period orbits parameterized by the energy.

A generalized Friedmann-Robertson-Walker Hamiltonian system is studied in dimension 6. The averaging theory is the tool used to provide sufficient conditions on the six parameters of the system which guarantee the existence of continuous families of period orbits parameterized by the energy.

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.