Alexander A History of Complex Dynamics

From Schröder to Fatou and Julia
1994
ISBN: 978-3-663-09197-4
Verlag: Vieweg & Teubner
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 24, 166 Seiten, eBook

Reihe: Aspects of Mathematics

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. Schröder (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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Alexander, Daniel S.

Inhaltsverzeichnis

Contents: Schröder, Cayley and Newton's Method - The Next Wave: Korkine and Farkas - Gabriel Koenigs - Iteration in the 1890's: Grévy - 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 - Lattès and Ritt - Fatou and Julia.

Über Autor(innen)

Daniel S. Alexander ist Professor an der Drake University, Des Moines, Iowa, USA.