The local study of iterated holomorphic mappings, in a neighborhood of a fixed point, was quite well developed in the late 19th century. (Compare §§8–10, and see Alexander.) However, except for one very simple case studied by Schroder and Cayley (see Problem 7-a), nothing was known about the global behavior of iterated holomorphic maps until 1906, when Pierre Fatou described the following startling example. For the map z ↦ z 2/(z 2 + 2), he showed that almost every orbit under iteration converges to zero, even though there is a Cantor set of exceptional points for which the orbit remains bounded away from zero. (Problems 4-e, f.) This aroused great interest. After a hiatus during the first world war, the subject was taken up in depth by Fatou, and also by Gaston Julia and others such as S. Lattes and J. F. Ritt. The most fundamental and incisive contributions were those of Fatou himself. However Julia was a determined competitor, and tended to get more credit because of his status as a wounded war hero. (In 1918, Julia was awarded the “Grand Prix des Sciences Mathematiques” by the Paris Academy of Sciences for his work.)