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A History of Complex Dynamics

From Schröder to Fatou and Julia

  • Textbook
  • © 1994

Overview

Authors:
  1. Daniel S. Alexander

    1. Department of Mathematics, Drake University, Des Moines, USA

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Part of the book series: Aspects of Mathematics (ASMA, volume 24)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-2
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  2. Schröder, Cayley and Newton’s Method

    • Daniel S. Alexander
    Pages 3-22

  3. The Next Wave: Korkine and Farkas

    • Daniel S. Alexander
    Pages 23-36

  4. Gabriel Koenigs

    • Daniel S. Alexander
    Pages 37-52

  5. Iteration in the 1890’s: Grévy

    • Daniel S. Alexander
    Pages 53-59

  6. Iteration in the 1890’s: Leau

    • Daniel S. Alexander
    Pages 60-74

  7. The Flower Theorem of Fatou and Julia

    • Daniel S. Alexander
    Pages 75-83

  8. Fatou’s 1906 Note

    • Daniel S. Alexander
    Pages 84-95

  9. Montel’s Theory of Normal Families

    • Daniel S. Alexander
    Pages 96-107

  10. The Contest

    • Daniel S. Alexander
    Pages 108-116

  11. Lattès and Ritt

    • Daniel S. Alexander
    Pages 117-123

  12. Fatou and Julia

    • Daniel S. Alexander
    Pages 124-142

  13. Back Matter

    Pages 143-166
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Keywords

About this book

In late 1917 Pierre Fatou and Gaston Julia each announced several results regarding the iteration ofrational functions of a single complex variable in the Comptes rendus of the French Academy of Sciences. These brief notes were the tip of an iceberg. In 1918 Julia published a long and fascinating treatise on the subject, which was followed in 1919 by an equally remarkable study, the first instalIment of a three­ part memoir by Fatou. Together these works form the bedrock of the contemporary study of complex dynamics. This book had its genesis in a question put to me by Paul Blanchard. Why did Fatou and Julia decide to study iteration? As it turns out there is a very simple answer. In 1915 the French Academy of Sciences announced that it would award its 1918 Grand Prix des Sciences mathematiques for the study of iteration. However, like many simple answers, this one doesn't get at the whole truth, and, in fact, leaves us with another equally interesting question. Why did the Academy offer such a prize? This study attempts to answer that last question, and the answer I found was not the obvious one that came to mind, namely, that the Academy's interest in iteration was prompted by Henri Poincare's use of iteration in his studies of celestial mechanics.

Authors and Affiliations

  • Department of Mathematics, Drake University, Des Moines, USA

    Daniel S. Alexander

About the author

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

Bibliographic Information

  • Book Title: A History of Complex Dynamics

  • Book Subtitle: From Schröder to Fatou and Julia

  • Authors: Daniel S. Alexander

  • Series Title: Aspects of Mathematics

  • DOI: https://doi.org/10.1007/978-3-663-09197-4

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Fachmedien Wiesbaden 1994

  • Softcover ISBN: 978-3-663-09199-8Published: 20 November 2013

  • eBook ISBN: 978-3-663-09197-4Published: 29 June 2013

  • Series ISSN: 0179-2156

  • Edition Number: 1

  • Number of Pages: VIII, 166

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Engineering, general

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