Poincare and the Three Body Problem

Couverture
American Mathematical Soc., 1997 - 272 pages
Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm.
Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics.
 

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Table des matières

Introduction
1
Introduction
5
Notations et définitions
14
Théorie des invariants intégraux
46
Exposants caractéristiques
58
Solutions périodiques des équations de la dynamique
65
Poincarés Memoir on the Three Body Problem
71
Calcul des exposants caractéristiques
80
Etude des cas où il ny a que deux degrés de liberté
166
Associated Mathematical Activity
175
Hadamard and Birkhoff
199
Epilogue
219
A letter from Gösta MittagLeffler
227
Entries received in the Oscar Competition
233
Title Pages and Tables of Contents
239
Solutions asymptotiques 88
242

Théorie des solutions périodiques
88
Reception of Poincarés Memoir
133
Poincarés Related Work after 1889
151
Theorems in P1 not included in P2
247
Droits d'auteur

Expressions et termes fréquents

Informations bibliographiques