  We consider the effect of a non-autonomous periodic perturbation on a 2-dof
autonomous system obtained as a truncation of the Hamiltonian-Hopf normal form.
Our analysis focuses on the behaviour of the splitting of the invariant
2-dimensional stable/unstable manifolds. We analyse the different changes of
dominant harmonic in the splitting functions. We describe how the dominant
harmonics depend on the quotients of the continuous fraction expansion of the
periodic forcing frequency. We have considered different frequencies including
quadratic irrationals, frequencies having continuous fraction expansion with
bounded quotients and frequencies with unbounded quotients. The methodology
used is general enough to systematically deal with all these frequency types.
All together allow us to get a detailed description of the asymptotic splitting
behaviour for the concrete perturbation considered.
