Families of multi-round homoclinic and periodic orbits near a saddle-center equilibrium

We consider a real analytic two degrees of freedom Hamiltonian system possessing a homoclinic orbit to a saddle-center equilibrium $p$ (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such a system and show that in the case of nonresonance there are countable sets of multi-round homoclinic orbits to $p$. We also find families of periodic orbits, accumulating a the homoclinic orbits.