On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom

Agraïments: The second author is partially supported by CNPq grant 304926/2009-4 and by FAPEMIG grant PPM-00204-11. The authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.We study periodic orbits of Hamiltonian differential systems with three degrees of freedom using the averaging theory. We have chosen the classical integrable Hamiltonian system with the Hooke potential and we study periodic orbits which bifurcate from the periodic orbits of the integrable system perturbed with a non-autonomous potential