On the iteration of rational functions

Abstract

Notes on the iteration of rational functions have been published in the C o m p t e s R e n d u s during the last few years by Julia, Fatou, Lattes, and myself.t Many of the results announced were obtained independently by more than one writer, the priority in such cases seeming to belong to Julia. I wish to present here that small part of my work which has not been covered by the other writers, postponing until after the appearance of their memoirs the publication of such of my other results as may still be of interest.: The pth iterate of the analytic function f (x) will be denoted by fp (x). If f ( c) = c, the point c will be called a fixed point of f ( x) . Let the Taylor development of f ( x) at the fixed point c be