## Celestial Encounters: The Origins of Chaos and Stability
Starting with the story of Poincar 's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincar . More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it. |

### What people are saying - Write a review

### Contents

A Great DiscoveryAnd a Mistake | 3 |

A WALK in PARIS | 4 |

NEWTONS INSIGHT | 7 |

A LANGUAGE for the LAWS of NATURE | 9 |

MODELS of REALITY | 13 |

MANIFOLD WORLDS | 18 |

THE nBODY PROBLEM | 20 |

KING OSCARS PRIZE | 23 |

ENCOUNTERS at a CONFERENCE | 112 |

FROM FOUR to FIVE BODIES | 113 |

THE END of a CENTURYS QUEST | 116 |

A SYMMETRIC DIGRESSION | 122 |

AN IDEA at DINNER | 123 |

Stability | 127 |

A LONGING for ORDER | 128 |

THE MARQUIS and the EMPEROR | 131 |

POINCARES ACHIEVEMENT | 27 |

LES MÉTHODES NOUVELLES | 30 |

FIXED POINTS | 31 |

FIRST RETURNS | 34 |

A GLIMPSE OF CHAOS | 37 |

PANDORAS BOX | 42 |

POINCARES MISTAKE | 44 |

A SURPRISING DISCOVERY | 48 |

Symbolic Dynamics | 51 |

ON THE BEACH AT RIO | 55 |

SMALES HORSESHOE | 60 |

SHIFTS on SYMBOLS | 65 |

SYMBOLS for CHAOS | 68 |

OSCILLATIONS and REVOLUTIONS | 73 |

A NEW SCIENCE? | 78 |

A SINGULAR MAN | 82 |

COLLISION or BLOWUP | 88 |

COMPUTER GAMES | 91 |

HOW to CATCH a RABBIT | 96 |

A MEASURE of SUCCESS | 101 |

REGULARIZING COLLISIONS | 104 |

CELESTIAL BILLIARDS | 106 |

MUSIC of the SPHERES | 135 |

ETERNAL RETURN | 139 |

PERTURBING the WORLD | 143 |

How STABLE is STABLE? | 147 |

LINEARIZATION and ITS LIMITS | 153 |

THE STABILITY of MODELS | 157 |

PLANETS in BALANCE | 159 |

KAM Theory | 164 |

SIMPLIFY and SOLVE | 165 |

QUASIPERIODIC MOTIONS | 170 |

PERTURBING the TORI | 174 |

LETTERS a LOST SOLUTION and POLITICS | 177 |

WORRYING at the PROOF | 182 |

TWIST MAPS | 187 |

A GIFTED STUDENT | 190 |

CHAOS DIFFUSES | 193 |

EPILOGUE | 201 |

Notes | 203 |

Bibliography | 213 |

225 | |

### Other editions - View all

Celestial Encounters: The Origins of Chaos and Stability Florin Diacu,Philip Holmes No preview available - 1996 |