In this paper we prove the breakdown of the two-dimensional stable andunstable manifolds associated to two saddle-focus points which appear in theunfoldings of the Hopf-zero singulariry. The method consists in obtaining anasymptotic formula for the difference between this manifolds which turns to beexponentially small respect to the unfolding parameter. The formula obtained isexplicit but depends on the so-called Stokes constants, which arise in thestudy of original vector field and which corresponds to the so called innerequation in singular perturbation theory.
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