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The Mathematical Intelligencer

, Volume 18, Issue 3, pp 66–70 | Cite as

The solution of then-body problem

  • Florin Diacu
Article

Keywords

Series Solution Triple Collision German Mathematician Differential Equation Theory Newtonian Gravitational System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [A]
    K.G. Andersson, Poincaré’s discovery of homoclinic points,Archive for History of Exact Sciences 48 (1994), 133–147.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [BG]
    J. Barrow-Green, Oscar II’s prize competition and the error in Poincaré’s memoir on the three body problem,Archive for History of Exact Sciences 48 (1994), 107–131.CrossRefMathSciNetGoogle Scholar
  3. [B]
    J. Bernoulli,Opera Omnia, vol. I, Georg Olms Verlagsbuchandlung, Hildesheim, 1968.zbMATHGoogle Scholar
  4. [Bi]
    G. Bisconcini, Sur le problème des trois corps,Acta Mathematica 30 (1906), 49–92.CrossRefMathSciNetGoogle Scholar
  5. [Br]
    E.H. Bruns, Über die Integrale des Vielkörper-Problems,Acta Mathematica 11 (1887), 25–96.CrossRefMathSciNetGoogle Scholar
  6. [CJZ]
    C. Calude, H. Jürgensen and M. Zimand, Is independence an exception?Applied Math. Comput. 66 (1994), 63–76.CrossRefzbMATHGoogle Scholar
  7. [D1]
    F.N. Diacu,Singularities of the N-Body Problem, Les Publications CRM, Montréal, 1992.zbMATHGoogle Scholar
  8. [D2]
    F.N. Diacu, Painlevé’s conjecture,The Mathematical Intelligencer 15 (1993), no. 2, 6–12.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [DH]
    F.N. Diacu and P. Holmes,Celestial Encounters—The Origins of Chaos and Stability. Princeton University Press (to appear in August 1996).Google Scholar
  10. [Di]
    Dieudonné, J.,A History of Algebraic and Differential Topology 1900-1960, Birkhäuser, Boston, Basel, 1989.Google Scholar
  11. [G]
    R.L. Goodstein,Essays in the Philosophy of Mathematics, Leicester University Press, 1965.Google Scholar
  12. [Go]
    K. Godei, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Système,Monatshefte für Mathematik und Physik 38 (1931), 173–198.Google Scholar
  13. [P]
    H. Poincaré,New Methods of Celestial Mechanics (with an introduction by D.L. Goroff), American Institute of Physics, 1993.Google Scholar
  14. [S]
    D.G. Saari, A visit to the Newtonian N-body problem via elementary complex variables,The American Mathematical Monthly 97 (1990), 105–119.CrossRefzbMATHMathSciNetGoogle Scholar
  15. [Si]
    C.L. Siegel, Der Dreierstoß,Annals of Mathematics 42 (1941), 127–168.CrossRefMathSciNetGoogle Scholar
  16. [Sul]
    K. Sundman, Recherches sur le problème des trois corps,Acta Societatis Scientiarum Fennicae 34 (1907), no. 6.Google Scholar
  17. [Su2]
    K. Sundman, Nouvelles recherches sur le problème des trois corps,Acta Societatis Scientiarum Fennicae 35 (1909), no. 9.Google Scholar
  18. [Su3]
    K. Sundman, Mémoire sur le problème des trois corps,Acta Mathematica 36 (1912), 105–179.CrossRefzbMATHMathSciNetGoogle Scholar
  19. [U]
    J.B. Urenko, Improbability of collisions in Newtonian gravitational systems of specified angular momentum.SIAM f. Appl. Math. 36 (1979), 123–147.CrossRefzbMATHMathSciNetGoogle Scholar
  20. [Wa]
    Q. Wang, The global solution of the n-body problem,Celestial Mechanics 50 (1991), 73–88.CrossRefzbMATHGoogle Scholar
  21. [W]
    A. Wintner,The Analytical Foundations of Celestial Mechanics, Princeton University Press, Princeton, NJ, 1941.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 1996

Authors and Affiliations

  • Florin Diacu
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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