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A global existence theorem for the four body problem of Newtonian mechanics. (English) Zbl 0353.70008


MSC:

70F10 \(n\)-body problems
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:

[1] Abraham, R., Foundations of Mechanics (1967), Benjamin: Benjamin New York
[2] Mather, J.; McGehee, R., (Proceedings of Bat. Conference. Proceedings of Bat. Conference, Seattle (1974))
[3] Marchal, C.; Saari, D. G., On the final evolution of the \(n\)-body problem, J. Differential Equations, 20, 150-186 (1976) · Zbl 0336.70010
[4] Marchal, C.; Saari, D. G., Hill Regions for the general three-body problem, Celestial Mechanics, 12, 115-129 (1975) · Zbl 0323.70009
[5] Painlevé, P., Lecons sur la théorie analytique des équations différentielles (1897), Hermann: Hermann Paris · JFM 28.0262.01
[6] Pollard, H., A Mathematical Introduction to Celestial Mechanics (1967), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J. · Zbl 0141.23803
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[9] Saari, D. G., Collisions are of first category, (Proc. Amer. Math. Soc., 47 (1975)), 442-445 · Zbl 0298.70005
[10] Saari, D. G., Singularities of Newtonian gravitational systems, (Peixoto, M. M., Dynamical Systems (1973), Academic Press: Academic Press New York), 479-487
[11] Saari, D. G., Singularities and collisions of Newtonian gravitational systems, Arch. Rational Mech. Math., 49, 311-320 (1973) · Zbl 0253.70010
[12] Saari, D. G., Expanding gravitational systems, Trans. Amer. Math. Soc., 156, 219-240 (1971) · Zbl 0215.57001
[13] Sperling, H., On the real singularities of the \(n\)-body problem, J. Reine Angew. Math., 245, 15-40 (1970) · Zbl 0207.23301
[14] J. UrenkoSIAM J. Appl. Math.; J. UrenkoSIAM J. Appl. Math. · Zbl 0408.70011
[15] von Zeipel, H., Sur les singularités du problème des \(n\) corps, Ark. Mat. Astron. Fys., 4 (1908) · JFM 39.0792.14
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