EAN: 9783663091998

A HISTORY OF COMPLEX DYNAMICS - DANIEL S ALEXAN...

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.

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