Complete classification of 2-ramified power series

In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics p. Let g be such a series, then g has a fixed point at the origin and the corresponding lower ramification numbers of g are then, up to a constant, the degree of the first non-linear term of p-power iterates of g. The result is a complete classification of power series g having ramification numbers of the form 2(1 + p + · · · + p^n). Furthermore, in proving said classification we explicitly compute the first significant terms of g at its pth iterate.