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A History of Complex Dynamics

From Schröder to Fatou and Julia

  • Daniel S. Alexander

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

Table of contents

  1. Front Matter
    Pages i-2
  2. Daniel S. Alexander
    Pages 3-22
  3. Daniel S. Alexander
    Pages 23-36
  4. Daniel S. Alexander
    Pages 37-52
  5. Daniel S. Alexander
    Pages 53-59
  6. Daniel S. Alexander
    Pages 60-74
  7. Daniel S. Alexander
    Pages 75-83
  8. Daniel S. Alexander
    Pages 84-95
  9. Daniel S. Alexander
    Pages 96-107
  10. Daniel S. Alexander
    Pages 108-116
  11. Daniel S. Alexander
    Pages 117-123
  12. Daniel S. Alexander
    Pages 124-142
  13. Back Matter
    Pages 143-166

About this book

Introduction

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.

Keywords

dynamics flow history

Authors and affiliations

  • Daniel S. Alexander
    • 1
  1. 1.Department of MathematicsDrake UniversityDes MoinesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-663-09197-4
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1994
  • Publisher Name Vieweg+Teubner Verlag, Wiesbaden
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-663-09199-8
  • Online ISBN 978-3-663-09197-4
  • Series Print ISSN 0179-2156
  • Buy this book on publisher's site
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