On the dynamics of some diffeomorphisms of C2 near parabolic fixed points

In this paper we consider diffeomorphisms of C-2 of the special form F(z, w) = (w, -z + 2G(w)). For such maps the origin is a parabolic fixed point. Under certain hypotheses on G we prove the existence of a domain Omega subset of C with 0 is an element of partial derivative Omega and of invariant complex curves w = f(z) and w = g(z), z is an element of Omega, for F-1 and F, such that F-n(z,f(z)) --> 0 and F-n(z,g(z)) --> 0 as n --> infinity.