Poincaré and the Three Body Problem, Volume 2

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American Mathematical Soc., 1997 - 272 pages
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The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincare, on a problem in celestial mechanics: the three body problem. This ancient problem--to describe the paths of three bodies in mutual gravitational interaction--is one of those which is simple to pose but impossible to solve precisely. 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 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
Historical Background
7
Propriltes generates des Equations difterentielles
8
Notations et definitions
9
Poincares Work before 1889
29
Thdorie des invariants intgraux
40
Oscar IIs 60th Birthday Competition
49
Rxposants caracteristiques
58
Etude du cas ou il ny a que deux degres de libertc
97
Reception of Poincares Memoir
133
Poincares Related Work after 1889
151
Associated Mathematical Activity
175
Hadamard and Birkhoff
199
Epilogue
219
A letter from Gosta MittagLeffler
227
Entries received in the Oscar Competition
233

Solutions p5riodiques des Equations de la dynamiquo
65
Poincares Memoir on the Three Body Problem
71
Calcnl des exposants caraolristiijues
80
Solutions asymptotiques
88
Title Pages and Tables of Contents
239
Theorems in PI not included in P2
247
Droits d'auteur

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