Diacu, Florin The solution of the \(n\)-body problem. (English) Zbl 0892.70007 Math. Intell. 18, No. 3, 66-70 (1996). The author gives an historical retrospection of the \(n\)-body problem (and of its solution). He describes the intriguing story and unexpected consequences of the most important attempts to obtain an explicit solution. The \(n\)-body problem has posed and continues to pose new challenges. Reviewer: M.Gousidou-Koutita (Thessaloniki) Cited in 2 ReviewsCited in 12 Documents MSC: 70F10 \(n\)-body problems 70-03 History of mechanics of particles and systems Keywords:series solution PDFBibTeX XMLCite \textit{F. Diacu}, Math. Intell. 18, No. 3, 66--70 (1996; Zbl 0892.70007) Full Text: DOI References: [1] Andersson, K. G., Poincaré’s discovery of homoclinic points, Archive for History of Exact Sciences, 48, 133-147 (1994) · Zbl 0812.01011 [2] Barrow-Green, J., Oscar II’s prize competition and the error in Poincaré’s memoir on the three body problem, Archive for History of Exact Sciences, 48, 107-131 (1994) · Zbl 0812.01010 [3] Bernoulli, J., Opera Omnia (1968), Hildesheim: Georg Olms Verlagsbuchandlung, Hildesheim · Zbl 0195.00703 [4] G., Bisconcini, Sur le problème des trois corps, Acta Mathematica, 30, 49-92 (1906) · JFM 36.0773.03 [5] Bruns, E. H., Über die Integrale des Vielkörper-Problems, Acta Mathematica, 11, 25-96 (1887) · JFM 19.0935.01 [6] Calude, C.; Jürgensen, H.; Zimand, M., Is independence an exception, Applied Math. Comput., 66, 63-76 (1994) · Zbl 0822.03024 [7] Diacu, F. N., Singularities of the N-Body Problem (1992), Montréal: Les Publications CRM, Montréal · Zbl 0754.70009 [8] Diacu, F. N., Painlevé’s conjecture, The Mathematical Intelligencer, 15, 2, 6-12 (1993) · Zbl 0769.70011 [9] F.N. Diacu and P. Holmes,Celestial Encounters—The Origins of Chaos and Stability. Princeton University Press (to appear in August 1996). · Zbl 0944.37001 [10] J., Dieudonné,, A History of Algebraic and Differential Topology (1989), Boston, Basel: Birkhäuser, Boston, Basel · Zbl 0673.55002 [11] R.L. Goodstein,Essays in the Philosophy of Mathematics, Leicester University Press, 1965. · Zbl 0144.24301 [12] Godei, K., Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Système, Monatshefte für Mathematik und Physik, 38, 173-198 (1931) · JFM 57.0054.02 [13] H. Poincaré,New Methods of Celestial Mechanics (with an introduction by D.L. Goroff), American Institute of Physics, 1993. [14] Saari, D. G., A visit to the Newtonian N-body problem via elementary complex variables, The American Mathematical Monthly, 97, 105-119 (1990) · Zbl 0748.70008 [15] Siegel, C. L., Der Dreierstoß, Annals of Mathematics, 42, 127-168 (1941) · JFM 67.0785.03 [16] Sundman, K., Recherches sur le problème des trois corps, Acta Societatis Scientiarum Fennicae, 34, 6 (1907) [17] Sundman, K., Nouvelles recherches sur le problème des trois corps, Acta Societatis Scientiarum Fennicae, 35, 9 (1909) · JFM 40.1017.07 [18] Sundman, K., Mémoire sur le problème des trois corps, Acta Mathematica, 36, 105-179 (1912) · JFM 43.0826.01 [19] Urenko, J. B., Improbability of collisions in Newtonian gravitational systems of specified angular momentum, SIAM f. Appl. Math., 36, 123-147 (1979) · Zbl 0408.70011 [20] Wang, Q., The global solution of the n-body problem, Celestial Mechanics, 50, 73-88 (1991) · Zbl 0726.70006 [21] Wintner, A., The Analytical Foundations of Celestial Mechanics (1941), Princeton, NJ: Princeton University Press, Princeton, NJ · Zbl 0026.02302 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.