  The late-stage formation of giant planetary systems is rich in interesting
dynamical mechanisms. Previous simulations of three giant planets initially on
quasi-circular and quasi-coplanar orbits in the gas disc have shown that highly
mutually inclined configurations can be formed, despite the strong eccentricity
and inclination damping exerted by the disc. Much attention has been directed
to inclination-type resonance, asking for large eccentricities to be acquired
during the migration of the planets. Here we show that inclination excitation
is also present at small to moderate eccentricities in two-planet systems that
have previously experienced an ejection or a merging and are close to resonant
commensurabilities at the end of the gas phase. We perform a dynamical analysis
of these planetary systems, guided by the computation of planar families of
periodic orbits and the bifurcation of families of spatial periodic orbits. We
show that inclination excitation at small to moderate eccentricities can be
produced by (temporary) capture in inclination-type resonance and the possible
proximity of the non-coplanar systems to spatial periodic orbits contributes to
maintaining their mutual inclination over long periods of time.
