Celestial Encounters: The Origins of Chaos and Stability / Edition 1

Celestial Encounters: The Origins of Chaos and Stability / Edition 1

by Florin Diacu, Philip Holmes
     
 

ISBN-10: 0691005451

ISBN-13: 9780691005454

Pub. Date: 03/08/1999

Publisher: Princeton University Press

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and

Overview

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos.

Starting with the story of Poincaré'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 Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations—the motions of the heavens—they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics.

In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

Product Details

ISBN-13:
9780691005454
Publisher:
Princeton University Press
Publication date:
03/08/1999
Series:
Princeton Science Library Series
Edition description:
New Edition
Pages:
256
Product dimensions:
6.10(w) x 9.20(h) x 0.50(d)

Table of Contents

Preface and Acknowledgments
A Note to the Reader
1. A Great Discovery - And a Mistake
2. Symbolic Dynamics
3. Collisions and Other Singularities
4. Stability
5. KAM Theory
Notes
Bibliography
Index

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