Daniel S. Alexander

A History of Complex Dynamics (eBook, PDF)

From Schröder to Fatou and Julia

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Vieweg+Teubner Verlag
• Seitenzahl: 166
• Erscheinungstermin: 29. Juni 2013
• Englisch
• ISBN-13: 9783663091974
• Artikelnr.: 53173257

Autorenporträt

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

Inhaltsangabe

1 Schröder, Cayley and Newton's Method.- 2 The Next Wave: Korkine and Farkas.- 3 Gabriel Koenigs.- 4 Iteration in the 1890's: Grévy.- 5 Iteration in the 1890's: Leau.- 6 The Flower Theorem of Fatou and Julia.- 7 Fatou's 1906 Note.- 8 Montel's Theory of Normal Families.- 9 The Contest.- 10 Lattès and Ritt.- 11 Fatou and Julia.