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
Théorie des invariants intégraux
Solutions périodiques des équations de la dynamique
Poincarés Memoir on the Three Body Problem
Calcul des exposants caractéristiques
Etude des cas où il ny a que deux degrés de liberté
Associated Mathematical Activity
Hadamard and Birkhoff
A letter from Gösta MittagLeffler
Entries received in the Oscar Competition
Title Pages and Tables of Contents
Solutions asymptotiques 88
Théorie des solutions périodiques
Reception of Poincarés Memoir
Poincarés Related Work after 1889
Theorems in P1 not included in P2
Acta analysis analytic analytic continuation approximation astronomers asymptotic series asymptotic solutions asymptotic surfaces behaviour Birkhoff celestial mechanics Chapter characteristic exponents closed curve closed geodesics coefficients collision competition considered constant coordinates corresponding Darwin defined derived differential equations discussion divergent divergent series doubly asymptotic dynamical systems expanded in powers finite Furthermore geometric George Birkhoff given Gyldén Hadamard Hamiltonian systems Hermite Hill's IM-L important infinite number intersect invariant integral iterate Jacobian Kronecker Levi-Civita Liapunov Lindstedt's series lunar mathematical mathematician method Méthodes Nouvelles Mittag-Leffler's paper parameter particular periodic functions periodic orbits periodic solutions perturbation plane planetoid Poincaré began Poincaré's ideas Poincaré's memoir Poincaré's theorem positive prize proof proved the existence published qualitative question recurrent motion represented restricted problem restricted three body single-valued singular points solution curves stability Sundman theorem three body problem trajectory transformation transverse section trigonometric series uniformly convergent unstable variables Weierstrass zero