  Given a parabolic map in one dimension $f(z) = z+O(z^2)$, $f \neq Id$, it is
known that there exists the analogous of stable and unstable domains. That is,
domains in which every point is attracted by $f$ (and by the inverse $f^{-1}$)
towards the fixed point. In this paper we prove that there exists a natural
parametrization for the unstable manifold in terms of iterates for some subset
of parabolic maps. Furthermore, we prove that this parametrization is valid
also in the case of skew-product maps that satisfy certain conditions. Finally,
we give an application of this fact to construct Fatou disks for skew-product
maps that are parabolic in each direction.
