THE THEORY OF ITERATION OF RATIONAL FUNCTIONS goes back to the mid-nineteenth century and perhaps even to Abel. During its first classic period, it indissolubly linked the names of Pierre Fatou and Gaston Julia. It also generated great controversy accompanied by hasty anecdotes and schematic or fanciful stories. The account in Alexander 1994 is excellent: scholarly and balanced. But it is necessarily based on secondary published sources. I was closer. In fact, Julia was my teacher of differential geometry at École Polytechnique. More important were the stories told about him and Fatou by my uncle Szolem Mandelbrojt (1899–1983) and other persons I knew well. Combining what I heard and what it made me read, this chapter discusses Fatou, then Julia, and finally their interaction. The last section deals with the aftermath.
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