**History of Mathematics**

Volume: 11;
1997;
272 pp;
Softcover

MSC: Primary 01;
Secondary 70

Print ISBN: 978-0-8218-0367-7

Product Code: HMATH/11

List Price: $50.00

Individual Member Price: $40.00

**Electronic ISBN: 978-1-4704-3879-1
Product Code: HMATH/11.E**

List Price: $50.00

Individual Member Price: $40.00

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# Poincaré and the Three Body Problem

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*June Barrow-Green*

A co-publication of the AMS and the London Mathematical Society

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

#### Table of Contents

# Table of Contents

## Poincare and the Three Body Problem

- Cover Cover11
- Title page v6
- Dedication vii8
- Contents ix10
- Acknowledgements xi12
- Photograph and figure credits xiii14
- Chapter 1. Introduction 118
- Chapter 2. Historical background 724
- Chapter 3. Poincare’s work before 1889 2946
- Chapter 4. Oscar II’s 60th birthday competition 4966
- Chapter 5. Poincare’s Memoirs on the three body problem 7188
- Chapter 6. Reception of Poincare’s memoir 133150
- Chapter 7. Poincare’s related work after 1889 151168
- Chapter 8. Associated mathematical activity 175192
- Chapter 9. Hadamard and Birkoff 199216
- Chapter 10. Epilogue 219236
- Appendix 1. A letter from Gosta Mittag-Leffler to Sonya 227244
- Appendix 2. Announcement of the Oscar competition 229246
- Appendix 3. Entries recieved in the Oscar competition 233250
- Appendix 4. Report of the Prize commission 237254
- Appendix 5. Title pages and tables of contents 239256
- Appendix 6. Theorems in [P1] not included in [P2] 247264
- Index 267284
- Back Cover Back Cover1290

#### 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