Poincare and the Three Body ProblemAmerican 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 |
267 | |
Expressions et termes fréquents
Acta analysis analytic approximation astronomers asymptotic solutions asymptotic surfaces behaviour Birkhoff C₁ celestial mechanics Chapter characteristic exponents Charles Hermite closed curve closed geodesics coefficients collision competition Comptes Rendus considered constant convergent coordinates corresponding Darwin defined derived differential equations discussion divergent doubly asymptotic dynamical systems équations Euvres expanded in powers finite function Furthermore geometric George Birkhoff given Gyldén Hadamard Hamiltonian systems Henri Poincaré Hermite Hill's infinite number intersect invariant integral iterate Jacobian Jacques Hadamard Kronecker Levi-Civita Liapunov Lindstedt's series lunar mathematician method Méthodes Nouvelles Mittag-Leffler Mittag-Leffler's paper parameter particular periodic functions periodic orbits periodic solutions perturbation planetoid Poincaré's ideas Poincaré's memoir Poincaré's theorem positive prize problème des trois proof published qualitative question restricted problem restricted three body single-valued singular points solution curves stability Sundman theorem three body problem trajectory transformation transverse section trigonometric series trois corps uniformly convergent variables Weierstrass y₁ zero