## Poincaré and the Three Body Problem, 2. ciltThe 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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### İçindekiler

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 |

### Sık kullanılan terimler ve kelime öbekleri

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 contained coordinates corresponding defined derived differential equations discussion divergent divergent series doubly asymptotic dynamical systems error expanded in powers finite Furthermore generalisation geometric George Birkhoff given Gylden Hadamard Hamiltonian systems Hermite Hill's important infinite number intersection invariant integral iterate Jacobian Kronecker Levi-Civita Liapunov lunar mathematical mathematician Methodes Nouvelles Mittag-Leffler Mittag-Leffler's original paper parameter periodic functions periodic orbits periodic solutions perturbation plane planetoid Poincare began Poincare showed Poincare's memoir positive prize proof proved the existence published qualitative question represented restricted problem restricted three body satisfied single-valued singular points small divisors small values solution curves stability Sundman theorem three body problem trajectory transformation transverse section trigonometric series uniformly convergent variables volume Weierstrass zero