| Contents |
| We consider a Froeschl\'e type 4D map (depending on suitable parameters) which is close to the time-1 map of a 2-d.o.f. Hamiltonian vector field. This map models the dynamics in a double resonance. The map has an elliptic fixed point that eventually, for some parameters, becomes a complex-saddle. It is interesting to study the behavior of the splitting of the 2D invariant manifolds of the complex-saddle point. We will show the exponentially small character of such splitting for a limit Hamiltonian vector field. For the 4D symplectic map it turns out that such splitting shows up a completely different behavior, being like the splitting of a quasi-periodic forced Hamiltonian. The theoretical results will be illustrated with several numerical examples, which involve the computation of normal forms, invariant manifolds, splitting of the separatrices, ..., both for the related Hamiltonian vector field and for the 4D map. |
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