Abstract
A selective survey of then-body problem of celestial mechanics is given where the emphasis is on the asymptotic behavior of all solutions ast→∞, the possible configurations the particles can assume in phase space and in physical space, and collision and non-collision singularities.
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References
Chazy, J.: 1922,Ann. Sci. Ecole Norm. Sup. 39, 29–130.
Easton, R.: 1971,J. Diff. Eq. 10, 92.
Littlewood, J.: 1968,Some Problems in Real and Complex Analysis, Heath, Lexington, Mass.
Marchal, C.: 1971,Astron. Astrophys. 10, 278–289.
Marchal, C. and Saari, D. G.: 1975,Celes. Mech. 12, 115–129.
Marchal, C. and Saari, D. G.: 1976,J. Diff. Eq. 20, 150–186.
Mather, J. and McGehee, R.: 1975, Proceedings of Bat. Conference, Seatle, 1974.
Painlevé, P.: 1897,Lecons sur la théorie analytique des équations differentielles, Paris, A. Hermann.
Pollard, H.: 1966,Mathematical Introduction to Celestial Mechanics, Prentice-Hall.
Saari, D. G.: 1971a,Trans. Am. Math. Soc. 156, 219–240.
Saari, D. G.: 1971b,Trans. Am. Math. Soc. 162, 267–271.
Saari, D. G.: 1973a,Trans. Am. Math. Soc. 181, 351–368.
Saari, D. G.: 1973b,J. Diff. Eq. 14, 275–292.
Saari, D. G.: 1974, SIAMJ. Appl. Math. 26, 806–815.
Saari, D. G.: 1975,Proc. Am. Math. Soc. 47, 442–445.
Sitnikov, K.: 1960,Dokl. Akad. Nauk SSR 133, No. 2, 303–306.
Smale, S.: 1970,Invent. Math. 11, 45–64.
Sperling, H.: 1970,J. Reine Angew. Math. 245, 15–40.
Urenko, J.: 1975, Ph.D. dissertation, Northwestern University.
von Zeipel, H.: 1908,Ark. Mat. Astr. Fys. 4, No. 32.
Waldvogel, J.: 1975,Celes. Mech. 11, 429–432.
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Supported in part by NSF Grant MPS 71-03407 A03.
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Saari, D.G. TheN-body problem of celestial mechanics. Celestial Mechanics 14, 11–17 (1976). https://doi.org/10.1007/BF01247127
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DOI: https://doi.org/10.1007/BF01247127