A History of Complex Dynamics: From Schröder to Fatou and JuliaSpringer Science & Business Media, 29 de juny 2013 - 166 pàgines 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. |
Continguts
| 1 | |
Leau | 5 |
Korkine and Farkas | 23 |
Gabriel Koenigs | 37 |
Grévy | 53 |
The Flower Theorem of Fatou and Julia | 75 |
Fatous 1906 Note | 84 |
Montels Theory of Normal Families | 97 |
The Contest | 108 |
Lattès and Ritt | 123 |
| 143 | |
| 163 | |
Altres edicions - Mostra-ho tot
A History of Complex Dynamics: From Schröder to Fatou and Julia Daniel S. Alexander Visualització de fragments - 1994 |
A History of Complex Dynamics: From Schröder to Fatou and Julia Daniel S. Alexander Previsualització no disponible - 2013 |
Frases i termes més freqüents
Abel equation Abel's analytic function analytic iteration function approach arctan(iz Ascoli-Arzelà Theorem attracting fixed point behavior canonical Schröder equation Cayley Cayley's complex analytic functions complex dynamics complex functions conjugation converges under iteration converges uniformly curve Darboux defined Dirichlet principle disc discussed équations example exceptional values exists Fatou and Julia Fatou set fixed point theorem Flower Theorem function f(z given function global Grévy hebdomadaires des Séances implies infinitely integer interest iteration function iteration of complex Julia set Korkine l'Académie des Sciences Lattès Leau Leau's Lémeray linear fractional transformation mathematical mathématique meromorphic Montel's theory neighborhood Newton's method function normal families noted period p point Picard Theorems plane problem of analytic quadratic rational function regions Riemann sphere rigorous Ritt root of unity satisfies Schröder functional equation Séances de l'Académie sequence set theory solution F(z solve study of functional study of iteration TDP set Theorem 1.2 theory of normal uniform convergence