In this work we consider a normal form around a 1:-1 non semi-simple resonant periodic orbit
of a three-degree of freedom Hamiltonian system. From the formal analysis it can be proved the
branching off a two-parameter family of two-dimensional invariant tori, whose normal behavior
depends intrinsically on the Hamiltonian. Thus, only elliptic or elliptic, together with parabolic
and hyperbolic tori may detach form the resonant periodic orbit. Both patterns are mentioned in
the literature as the direct and, respectively, inverse Hopf bifurcations. Here we focus in the direct
case, which seems more interesting to us due to its immediate applications in Celestial Mechanics.
More precisely, our target is to prove the persistence of the (normally) elliptic invariant tori when
the whole Hamiltonian, and not only the truncated normal form is taking into account. Finally, and
as far as we know, none of the standard KAM results and methods apply directly to the situation
described above, so one needs to suite properly these techniques to the problem at hand
