Geometric location of periodic points of 2-ramified power series

Abstract

In this paper we study the geometric location of periodic points of power series defined over fields of positive characteristic p. We find a lower bound for the norm of all nonzero periodic points in the open unit disk of 2-ramified power series. We prove that this bound is optimal for a large class of power series. Our main technical result is a computation of the first significant terms of p-power iterates of 2-ramified power series. As a by-product we obtain a self-contained proof of the characterization of 2-ramified power series.