A history of complex dynamics : from Schröder to Fatou and Julia
著者
書誌事項
A history of complex dynamics : from Schröder to Fatou and Julia
（Aspects of mathematics = Aspekte der Mathematik, E ; vol. 24）
Vieweg, c1994
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注記
Includes bibliographical reference (p. [143]-162) and index
内容説明・目次
内容説明
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.
目次
Contents: Schroder, Cayley and Newton's Method - The Next Wave: Korkine and Farkas - Gabriel Koenigs - Iteration in the 1890's: Grevy - Iteration in the 1890's: Leau - The Flower Theorem of Fatou and Julia - Fatou's 1906 Note - Montel's Theory of Normal Families - The Contest - Lattes and Ritt - Fatou and Julia.
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