Poincare and the Three Body Problem

Couverture
American Mathematical Soc., 1997 - 272 pages
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 Poincaré, 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. Poincaré's famous memoir on the three body problem arose from his entry in King Oscar of Sweden's 60th birthday competition. 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 Poincaré discoverd mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincaré and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincaré'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 Poincaré's subsequent highly influential work in celestial mechanics. Co-published with the London Mathematical Society.
 

Table des matières

Introduction
1
Historical Background
7
Poincarés Work before 1889
29
Oscar IIs 60th Birthday Competition
49
6
65
Poincarés Memoir on the Three Body Problem
71
Reception of Poincarés Memoir
133
Poincarés Related Work after 1889
151
Epilogue
219
A letter from Gösta MittagLeffler
227
Entries received in the Oscar Competition
233
Title Pages and Tables of Contents
239
Introduction
242
Theorems in P1 not included in P2
247
Théorie des solutions périodiques
263
9
267

Associated Mathematical Activity
175
Hadamard and Birkhoff
199

Expressions et termes fréquents

Informations bibliographiques