Quasi-parabolic analytic transformations of Cn

Let F be an analytic transformation of Cn, with the origin O as a quasi-parabolic fixed point. We will associate an invariant, order ν(F), to F and study the local dynamics of F when it has a non-degenerate characteristic direction [v] and is dynamically separating in the direction [v]. We show that for such F there exist at least ν(F)−1 parabolic curves tangent to [v] at the origin. We also study a non-dynamically-separating example in details.