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Oscar II’s prize competition and the error in Poincaré’s memoir on the three body problem. (English) Zbl 0812.01010

From the introduction: “In the autumn of 1890 Henri Poincaré’s memoir on the three body problem was published in the journal Acta Mathematica as the winning entry in the international prize competition sponsored by Oscar II, King of Sweden and Norway, to mark his 60th birthday on January 21, 1889. Today Poincaré’s published memoir is renowned both for providing the foundations for his celebrated three-volume Méthodes Nouvelles de la Mécanique Céleste and for containing the first mathematical description of chaotic behavior in a dynamical system.”
Correcting an error in his memoir Poincaré discovered the existence of what today are known as homoclinic points. As a result the memoir which appeared in Acta was remarkable different from the one which had actually won the prize almost two years earlier.

MSC:

01A55 History of mathematics in the 19th century
70F07 Three-body problems
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References:

[1] H. Poincaré: ?Sur le probléme des trois corps et les équations de la dynamique? Acta Mathematica 13 (1890), 1-270 = ?uvres 7, 262-479. · JFM 22.0907.01
[2] H. Poincaré: Les Méthodes Nouvelles de la Mécanique Céleste I?III, 1892-1899, Gauthier Villars, Paris.
[3] Y. Domar: ?On the foundation of Acta Mathematica? Acta Mathematica 148 (1982), 3-8. · Zbl 0488.01006
[4] I. Grattan-Guinness: ?Materials for the history of mathematics in the Institute of Mittag-Leffler? Acta Mathematica 62 (1971), 363-374. · Zbl 0238.01025
[5] G. Mittag-Leffler: ?Zur Biographie von Weierstrass? Acta Mathematica 38 (1912), 29-65. · JFM 42.0017.04
[6] C. Hermite: ?Lettres de Charles Hermite à Gosta Mittag-Leffler (1884-1891)? Cahiers de Seminaires d’Histoire des Mathématiques 6 (1985), 79-217.
[7] K.-R. Biermann: ?Die Mathematik und ihre Dozenten an der Berliner Universität 1810-1933? 1988, Akademie-Verlag, Berlin. · Zbl 0208.28802
[8] L. Kronecker: ?Bemerkungen über Dirichlet’s letzte Arbeiten? Sitzungesberichte der Königlich Preussischen Akademie der Wissenschaften 1888, 439-442 = Werke V, 471-476. · JFM 20.0014.02
[9] H. Poincaré: ?Lettres d’Henri Poincaré à M. Mittag-Leffler concernant le mémoire couronné du prix de S.M. Le Roi Oscar II?, Acta Mathematica 38 (1921), 161-173.
[10] H. Gyldén: ?Untersuchungen über die Convergenz der Reigen, welche zur Darstellung der Coordinaten der Planeten angewendet werden? Acta Mathematica 9 (1887), 185-294. · JFM 19.1208.03
[11] E. Phragmén: ?Poincaré’ska fallet af tekropparsproblemet? (=On some dynamical problems which are related to the restricted three body problem) K.V.A. Bihang till Handlingar 15 (1) No. 13 (1889), 1-33.
[12] H. Poincaré: ?Mémoire sur les courbes définies par une équation différentielle? Journal de Mathématiques (3) 7 (1881), 375-422; 8 (1882), 251-296; Journal de Mathématiques Pure et Appliquées (4) 1 (1885), 167-244; 2 (1886), 151-217 = ?uvres I, 3-44, 44-84, 90-161; 167-222. · JFM 13.0591.01
[13] E. T. Whittaker: ?Report on the progress of the solution of the problem of three bodies?, BAAS Report 1899, 121-159.
[14] R. Marcolongo: ?Il problema dei tre corpi da Newton (1686) al nostri giorni?, 1919, Hoepli, Milan. · JFM 47.0834.12
[15] J. Liouville: ?Note sur la théorie de la variation des constantes arbitraires? Journal de Mathématiques Pures et Appliquées 3 (1838), 342-349.
[16] L. Boltzmann: ?Ueber die Druckkräfte, welche auf Ringe wirksam sind, die in bewegte Flüssigkeit tauchen? Journal für die Reine und Angewandte Mathematik 73 (1871), 111-134. · JFM 03.0451.01
[17] H. Poincaré: ?Sur un méthode de M. Lindstedt? Bulletin Astronomique 3 (1886), 57-61 = ?uvres 7, 546-560.
[18] K. Bohlin: ?Zur Frage der Convergenz der Reihenentwickelungen in der Störungstheorie? Astronomische Nachrichten 121 (1888), 17-24. · JFM 21.1223.03
[19] H. Poincaré: ?Sur les intégrales irrégulières des équations linéaires? Acta Mathematica 8 (1886), 295-344 = ?uvres I, 290-332. · JFM 18.0273.02
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