Poincare and the Three Body Problem
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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Notations et définitions
Poincarés Work before 1889
Théorie des invariants intégraux
Oscar IIs 60th Birthday Competition
Etude du cas où il ny a que deux degrés de liberté
Reception of Poincarés Memoir
Poincarés Related Work after 1889
Associated Mathematical Activity
Hadamard and Birkhoff
A letter from Gösta MittagLeffler
Entries received in the Oscar Competition
Poincarés Memoir on the Three Body Problem
Calcul des exposants caractéristiques
Title Pages and Tables of Contents
Theorems in P1 not included in P2
Acta analysis analytic appeared application approach approximation asymptotic began Birkhoff called celestial mechanics Chapter closed coefficients competition complete concerned considered constant contained continued convergent coordinates corresponding curve defined dependent derived described detailed determined differential equations direction discussion distance divergent dynamical error established existence expanded expression extended fact Figure final finite function further gave geodesics give given Gyldén Hadamard Hamiltonian Hermite Hill Hill's idea important included infinite initial interest introduction invariant integral involved known later limit mathematical mean memoir method Mittag-Leffler motion move nature Note orbits original particular periodic solutions perturbation Poincaré positive possible powers prize proof proved publication published question regard region remains represented respect satisfied showed singular space stability sufficiently surface theorem theory three body problem trajectory transformation values variables volume Weierstrass zero