  The aim of this work is to provide asymptotic estimates for the splitting of
separatrices in a perturbed 3-degree-of-freedom Hamiltonian system, associated
to a 2-dimensional whiskered torus (invariant hyperbolic torus) whose frequency
ratio is a quadratic irrational number. We show that the dependence of the
asymptotic estimates on the perturbation parameter is described by some
functions which satisfy a periodicity property, and whose behavior depends
strongly on the arithmetic properties of the frequencies.
