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The contemporary study of complex dynamics, which has flourished so
much in recent years, is based largely upon work by G. Julia (1918)
and P. Fatou (1919/20). The goal of this book is to analyze this
work from an historical perspective and show in detail, how it grew
out of a corpus regarding the iteration of complex analytic
functions. This began with investigations by E. Schroder (1870/71)
which he made, when he studied Newton's method. In the 1880's,
Gabriel Koenigs fashioned this study into a rigorous body of work
and, thereby, influenced a lot the subsequent development. But
only, when Fatou and Julia applied set theory as well as Paul
Montel's theory of normal families, it was possible to develop a
global approach to the iteration of rational maps. This book shows,
how this intriguing piece of modern mathematics became reality."
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