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Poincaré and the Three Body Problem
June Barrow-Green, The Open University, Milton Keynes, UK
A co-publication of the AMS and the London Mathematical Society.
cover
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History of Mathematics
1997; 272 pp; softcover
Volume: 11
Reprint/Revision History:
reprinted with corrections 1997; third printing 1999
ISBN-10: 0-8218-0367-0
ISBN-13: 978-0-8218-0367-7
List Price: US$47
Member Price: US$37.60
Order Code: HMATH/11
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The 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 Poincaré, 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.

Poincaré'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 Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm.

Poincaré and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincaré'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 Poincaré's subsequent highly influential work in celestial mechanics.

Readership

Graduate students, mathematicians, astronomers, and physicists interested in an historical perspective of mathematics.

Reviews

"Delightful and interesting to read ... will help professors ... provide some very interesting (and needed) historical background to their lectures. Any serious student of mathematical history will enjoy this treatise."

-- Applied Mechanics Reviews

"This is a superb piece of work and it throws new light on one of the most fundamental topics of mechanics ... This book can be thoroughly recommended."

-- Mathematical Reviews

"A fair treatment and a nice description of the history regarding Poincaré and the three body problem ... of interest to many mathematicians, physicists and astronomers ... a balanced and very readable book ... recommend[ed] ... to all mathematically trained people with an interest in the historical origins of chaos."

-- Nonlinear Science Today

"An interesting insight into the late 19th-century mathematical community and an account of [Poincaré's] memoirs' reception and impact ... clearly organized, well written, richly documented ... a highly valuable contribution to the history of modern mathematics, adding value to the series in which it appeared."

-- Zentralblatt MATH

"This book describes this history of the problem and of Poincaré's work, and it tells the fascinating story of (and behind) the Oscar Prize competition."

-- Monatshefte für Mathematik

"In a work of impressive scholarship, the author takes us through the history of the \(n\)-body problem from Newton to the present."

-- American Mathematical Monthly

Table of Contents

  • Introduction
  • Historical background
  • Poincaré's work before 1889
  • Oscar II's 60th birthday competition
  • Poincaré's memoir on the three body problem
  • Reception of Poincaré's memoir
  • Poincaré's related work after 1889
  • Associated mathematical activity
  • Hadamard and Birkhoff
  • Epilogue
  • Appendices
  • References
  • Index
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