This comtemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon the work of G. Julia (1918) and P. Fatou (1919-20). The book aims 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. Schroeder (1870-71) which he made when he studied Newton's method. In the 1880s, Gabriel Koenigs fashioned this study into a rigorous body of work, and thereby influenced a lot of the subsequent development. But only when Fatou and Julia applied set theory, as well as Paul Montel's theory of normal families, was it possible to develop a global approach to the iteration of rational maps. The book shows how this intriguing piece of modern mathematics became reality.
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4.0 out of 5 stars
Brief Book Review,
This review is from: A History of Complex Dynamics: From Schroder to Fatou and Julia (Aspects of Mathematics) (Hardcover)
Alexander's book is a very smart and well-written overview of this particular history-- one not told before at this length and in a book that even those not in the field can generally understand.
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