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El. knyga: Celestial Encounters: The Origins of Chaos and Stability

  • Formatas: 256 pages
  • Serija: Princeton Science Library
  • Išleidimo metai: 08-Dec-2020
  • Leidėjas: Princeton University Press
  • Kalba: eng
  • ISBN-13: 9780691221830
Kitos knygos pagal šią temą:
  • Formatas: 256 pages
  • Serija: Princeton Science Library
  • Išleidimo metai: 08-Dec-2020
  • Leidėjas: Princeton University Press
  • Kalba: eng
  • ISBN-13: 9780691221830
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Starting with the story of Poincare's work on the phenomenon of chaos, this study traces the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's "Principia" in 1686. In describing how mathematical rigour was brought to bear on one of our oldest fascinations - the motions of the heavens - they introduce the people whose ideas led to the field now called nonlinear dynamics. In presenting the modern theory of dynamic systems, the models underlying much of modern science are described pictorally, using the geometrical language invented by Poincare. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

Recenzijos

"One of Choice's Outstanding Academic Titles for 1997" "[ S]tories about the history of celestial mechanics are the subject of this delightful book. The authors interweave numerous anecdotes about the personalities involved in the discoveries with technical details of the mathematical ideas themselves. . . . a pleasant mix of things technical and things historical. . . . written in a lively and informative way."---Robert L. Devaney, Science "This book, which should be required reading for every nonspecialist astronomer, may well be headed toward becoming a classic." * Choice * "A particular strength of Celestial Encounters is the impression, conveyed with a deft touch, that mathematics is an international and collective effort made by real people for real reasons in the real world. All the players in the drama, alive or dead, come over as human beings who happen to have a passion for mathematics and an ability to fulfill that passion. This feature alone justifies buying the book."---Ian Stewart, New Scientist "A lively introduction to the fascinating story of celestial mechanics."---Jacques Laskar, Nature "Throughout the book one finds a vital quality that derives from the authors' real success in presenting mathematics as a human endeavor.... A valuable and accessible contribution to the chaos literature."---June Barrow-Green, Isis "A pleasant mix of things technical and things historical.... Written in a lively and informative way."---Robert Devaney, Science

Preface and Acknowledgments xi
A Note to the Reader xvii
A Great Discovery And a Mistake
A Walk in Paris
4(3)
Newton's Insight
7(2)
A Language for the Laws of Nature
9(4)
Models of Reality
13(5)
Manifold Worlds
18(2)
The n-Body Problem
20(3)
King Oscar's Prize
23(4)
Poincare's Achievement
27(3)
Les methodes nouvelles
30(1)
Fixed Points*
31(3)
First Returns*
34(3)
A Glimpse of Chaos*
37(5)
Pandora's Box
42(2)
Poincare's Mistake
44(4)
A Surprising Discovery
48(3)
Symbolic Dynamics
A Fixed Point Begins a Career
51(4)
On the Beach at Rio
55(5)
Smale's Horseshoe*
60(5)
Shifts on Symbols*
65(3)
Symbols for Chaos*
68(5)
Oscillations and Revolutions
73(5)
A New Science?
78(4)
Collisions and Other Singularities
A Singular Man
82(6)
Collision or Blowup
88(3)
Computer Games
91(5)
How to Catch a Rabbit
96(5)
A Measure of Success
101(3)
Regularizing Collisions
104(2)
Celestial Billiards
106(6)
Encounters at a Conference
112(1)
From Four to Five Bodies
113(3)
The End of a Century's Quest
116(6)
A Symmetric Digression
122(1)
An Idea at Dinner
123(5)
Stability
A Longing for Order
128(3)
The Marquis and the Emperor
131(4)
Music of the Spheres
135(4)
Eternal Return
139(4)
Perturbing the World
143(4)
How Stable is Stable?
147(1)
The Qualitative Age
147(6)
Linearization and Its Limits
153(4)
The Stability of Models
157(2)
Planets in Balance
159(6)
KAM Theory
Simplify and Solve
165(5)
Quasi-periodic Motions*
170(4)
Perturbing the Tori*
174(3)
Letters, a Lost Solution, and Politics
177(5)
Worrying at the Proof
182(5)
Twist Maps*
187(3)
A Gifted Student
190(3)
Chaos Diffuses
193(8)
Epilogue
201(2)
Notes 203(10)
Bibliography 213(12)
Index 225


Florin Diacu is Associate Professor of Mathematics at the University of Victoria in Canada. Philip Holmes, a Fellow of the American Academy of Arts and Sciences, is Professor of Mechanics and Applied Mathematics at Princeton University, where he directs the Program in Applied and Computational Mathematics.