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Singularities and collisions of Newtonian gravitational systems

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References

  1. Feller, W., An Introduction to Probability Theory and its Applications. Vol. 2. New York: J. Wiley 1966.

    Google Scholar 

  2. Painlevé, P., Leçons sur la théorie analytique des équations différentielles. Paris: A. Hermann 1897.

    Google Scholar 

  3. Pollard, H., & D. G. Saari, Singularities of the n-body problem, I. Arch. Rational Mech. and Math. 30, 263–269 (1968).

    Google Scholar 

  4. Pollard, H., & D. G. Saari, Singularities of the n-body problem, II. In: Inequalities-II, pp. 255–259. New York: Academic Press 1970.

    Google Scholar 

  5. Saari, D. G., Improbability of collisions in Newtonian gravitational systems. Trans. Amer. Math. Soc. 162, 267–271 (1971).

    Google Scholar 

  6. Saari, D. G., Improbability of collisions in Newtonian gravitational systems, II. To appear.

  7. Saari, D. G., Singularites of Newtonian gravitational systems. To appear in Proceedings of Symposium on Global Analysis, Dynamical Systems and Celestial Mechanics, Brazil, August, 1971.

  8. Siegel, C. L., & J. K. Moser, Lectures on Celestial Mechanics. Berlin-Göttingen-Heidelberg: Springer 1971.

    Google Scholar 

  9. Sperling, H., On the real singularities of the n-body problem. J. Reine Angew. Math. 245, 15–40 (1970).

    Google Scholar 

  10. Zeipel, H. Von, Sur les singularités du problème des n corps. Ark. Mat. Astr. Fys. 4, No. 32 (1908).

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 60201, Evanston, Illinois

    Donald G. Saari

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  1. Donald G. Saari
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Communicated by Mark Kac

This research was partially supported under National Scince Foundation grant GP 32116.

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Saari, D.G. Singularities and collisions of Newtonian gravitational systems. Arch. Rational Mech. Anal. 49, 311–320 (1973). https://doi.org/10.1007/BF00250511

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  • DOI: https://doi.org/10.1007/BF00250511

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