Celestial Encounters The Origins of Chaos and Stability
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
Princeton science library, v.119
1 online resource (258 p.).
9780691221830, 0691221839
1206398312
Cover Page
Half-title Page
Title Page
Copyright Page
Dedication Page
Contents
Preface and Acknowledgments
A Note to the Reader
1. A Great Discovery-And a Mistake
A Walk in Paris
Newton's Insight
A Language for the Laws of Nature
Models of Reality
Manifold Worlds
The n-Body Problem
King Oscar's Prize
Poincare's Achievement
Les methodes nouvelles
Fixed Points*
First Returns*
A Glimpse of Chaos*
Pandora's Box
Poincare's Mistake
A Surprising Discovery
2. Symbolic Dynamics
A Fixed Point Begins a Career On the Beach at Rio
Smale's Horseshoe*
Shifts on Symbols*
Symbols for Chaos*
Oscillations and Revolutions
A New Science?
3. Collisions and Other Singularities
A Singular Man
Collision or Blowup
Computer Games
How to Catch a Rabbit
A Measure of Success
Regularizing Collisions
Celestial Billiards
Encounters at a Conference
From Four to Five Bodies
The End of a Century's Quest
A Symmetric Digression
An Idea at Dinner
4. Stability
A Longing for Order
The Marquis and the Emperor
Music of the Spheres
Eternal Return Perturbing the World
How Stable is Stable?
The Qualitative Age
Linearization and Its Limits
The Stability of Models
Planets in Balance
5. KAM Theory
Simplify and Solve
Quasi-periodic Motions*
Perturbing the Tori*
Letters, a Lost Solution, and Politics
Worrying at the Proof
Twist Maps*
A Gifted Student
Chaos Diffuses
Enilosue
Notes
Bibliography
Index
Description based upon print version of record
public.eblib.com Click here to view book