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127:, and became the initial claim to fame for Poincaré himself. The detailed story behind these events, long forgotten, was brought back to life in a sequence of publications by multiple authors in the early and mid 1990s, including Barrow-Green's dissertation, a journal publication based on the dissertation, and this book.
84:, and the existence of orbits for those three bodies that remain stable over long periods of time. This problem has been of great interest mathematically since Newton's formulation of the laws of gravity, in particular with respect to the joint motion of the sun, earth, and moon. The centerpiece of
310:
calls it "the definitive work about the chaotic story of the King Oscar Prize" and "pleasantly accessible"; reviewer R. Duda calls it "clearly organized, well written, richly documented", and both Mawhin and Duda call it a "valuable addition" to the literature. And reviewer Albert C. Lewis writes
188:
and of the prize competition announced by Mittag-Leffler in 1885, which Barrow-Green suggests may have been deliberately set with
Poincaré's interests in mind and which Poincaré's memoir would win. The fifth chapter concerns Poincaré's memoir itself; it includes a detailed comparison of the
110:
and
Poincaré determined that there were serious errors in the paper. Poincaré called for the paper to be withdrawn, spending more than the prize money to do so. In 1890 it was finally published in revised form, and over the next ten years Poincaré expanded it into a monograph,
201:
of systems. After a chapter on
Poincaré's expanded monograph and his other later work on the three-body problem, the remainder of the book discusses the influence of Poincaré's work on later mathematicians. This includes contributions on the singularities of solutions by
319:-body problem) complains that Wang was omitted, that Barrow-Green "sometimes fails to see connections ... within Poincaré's own work" and that some of her translations are inaccurate, he also recommends the book.
290:
generalizing
Sundman's convergent series from three bodies to arbitrary numbers of bodies is also omitted. An epilogue considers the impact of modern computer power on the numerical study of Poincaré's theories.
189:
significant differences between the withdrawn and published versions, and overviews the new mathematical content it contained, including not only the possibility of chaotic orbits but also
303:, although the central part of the book, analyzing Poincaré's work, may be too light on mathematical detail to be readily understandable without reference to other material.
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Reviewer Ll. G. Chambers writes "This is a superb piece of work and it throws new light on one of the most fundamental topics of mechanics." Reviewer
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that it "provides insights into higher mathematics that justify its being on every university mathematics student's reading list". Although reviewer
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introduces the problem and its second chapter surveys early work on this problem, in which some particular solutions were found by Newton,
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This book is aimed at specialists in the history of mathematics, but can be read by any student of mathematics familiar with
49:
178:, and some special solutions of the three-body problem, and the fourth chapter surveys this history of the founding of
435:(as of February 2020, this site contains no review, only the book metadata and the Basic Library List recommendation).
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Sur le problème des trois corps et les équations de la dynamique
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as Volume 11 in their shared
History of Mathematics series (
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113:Les méthodes nouvelles de la mécanique céleste
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640:Bulletin of the London Mathematical Society
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424:"Poincaré and the Three Body Problem"
82:Newton's law of universal gravitation
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675:Poincaré and the Three-Body Problem
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554:Poincaré and the Three-Body Problem
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458:Poincaré and the Three-Body Problem
432:Mathematical Association of America
397:Poincaré and the Three-Body Problem
315:(himself a noted researcher on the
230:, on the stability of solutions by
132:Poincaré and the Three-Body Problem
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106:on the king's birthday, until
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597:The Mathematical Gazette
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718:1997 non-fiction books
571:10.1006/hmat.1999.2236
301:differential equations
295:Audience and reception
282:, V. K. Melnikov, and
208:Edvard Hugo von Zeipel
172:differential equations
30:history of mathematics
673:Duda, R., "Review of
276:George David Birkhoff
148:Joseph-Louis Lagrange
130:The first chapter of
125:convergence of series
121:dynamical astronomers
558:Historia Mathematica
402:Mathematical Reviews
186:Gösta Mittag-Leffler
152:Pierre-Simon Laplace
108:Lars Edvard Phragmén
44:. It was written by
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42:celestial mechanics
337:Mathematics portal
240:Forest Ray Moulton
232:Aleksandr Lyapunov
212:Tullio Levi-Civita
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92:, entitled
702:Categories
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323:References
260:KAM theory
216:Jean Chazy
199:invariants
195:integrals
123:over the
26:monograph
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