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. <P>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. <P>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.
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"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
"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
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This review is from: Poincare and the Three Body Problem (History of Mathematics, V. 11) (Paperback)
This book is somewhere between an historical essay and a blow-by-blow analysis of one of Poincare's most important papers, which gave rise to many significant developments in 20th-century mathematics. You have to really like the subject of differential equations to get into this.
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In November 1890 Henri Poincare's memoir on the three body problem was published in the journal Acta Mathematica as the winning entry in the international competition honoring the 60th birthday of Oscar II, King of Sweden and Norway. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nth consequent, doubly asymptotic trajectories, restreint des trois corps, asymptotic surfaces, arbitrary convex surface, last geometric theorem, doubly asymptotic solutions, noncollision singularities, recurrent motion, invariant integral, unstable periodic solution, three body problem, lunar perigee, small divisors, singular trajectories, closed geodesics, periodic solutions, lunar theory, restricted problem, dynamical astronomy, surface trajectory, characteristic exponents, recurrence theorem, perturbation function, infinite sheets Key Phrases - Capitalized Phrases (CAPs): (learn more)
Comptes Rendus, George Birkhoff, George Darwin, King Oscar, Acta Mathematica, American Mathematical Society, Jacques Hadamard, Karl Sundman, Equation of Asymptotic Surfaces, Simon Newcomb, Swedish Academy of Sciences, University of Stockholm New!
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In November 1890 Henri Poincare's memoir on the three body problem was published in the journal Acta Mathematica as the winning entry in the international competition honoring the 60th birthday of Oscar II, King of Sweden and Norway. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nth consequent, doubly asymptotic trajectories, restreint des trois corps, asymptotic surfaces, arbitrary convex surface, last geometric theorem, doubly asymptotic solutions, noncollision singularities, recurrent motion, invariant integral, unstable periodic solution, three body problem, lunar perigee, small divisors, singular trajectories, closed geodesics, periodic solutions, lunar theory, restricted problem, dynamical astronomy, surface trajectory, characteristic exponents, recurrence theorem, perturbation function, infinite sheets Key Phrases - Capitalized Phrases (CAPs): (learn more)
Comptes Rendus, George Birkhoff, George Darwin, King Oscar, Acta Mathematica, American Mathematical Society, Jacques Hadamard, Karl Sundman, Equation of Asymptotic Surfaces, Simon Newcomb, Swedish Academy of Sciences, University of Stockholm New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 26
books:
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- Biographical Memoirs: V.47 (Biographical Memoirs: A Series) by Office of the Home Secretary in Back Matter
- Mathematics and the Unexpected by Ivar Ekeland in Back Matter
- History of Mathematics, Vol. I (Dover Books on Mathematics) by David E. Smith in Back Matter
- Celestial Mechanics by Donald G. Saari in Back Matter
- New Methods of Celestial Mechanics (History of Modern Physics and Astronomy, Vol. 13) (3 Volumes) by Henri Poincare in Back Matter
See all 26 books this book cites
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