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Triple collision in the collinear three-body problem. (English) Zbl 0297.70011


MSC:

70F35 Collision of rigid or pseudo-rigid bodies
70F15 Celestial mechanics
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70F10 \(n\)-body problems
37N05 Dynamical systems in classical and celestial mechanics
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References:

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[9] Saari, D.: Singularities and collisions of newtonian gravitational systems. Arch. Rational Mech. Anal.49, 311-320 (1973) · Zbl 0253.70010 · doi:10.1007/BF00250511
[10] Sacker, R., Sell, G.: On the existence of nontrivial recurrent motions. Duke Math. J. to appear · Zbl 0274.54031
[11] Siegel, C.: Der Dreierstoß. Ann. Math.42, 127-168 (1941) · JFM 67.0785.03 · doi:10.2307/1968991
[12] Siegel, C., Moser, J.: Lectures on Celestial Mechanics. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0312.70017
[13] Sperling, H.: On the real singularities of then-body problem. J. Reine Angew. Math.245, 14-50 (1970) · Zbl 0207.23301
[14] Sundman, K.: Mémoire sur le problème des trois corps. Acta Math.36, 105-179 (1912) · JFM 43.0826.01 · doi:10.1007/BF02422379
[15] Sundman, K.: Nouvelles recherches sur le problème des trois corps Acta Soc. Sci. Feen.35, No. 9 (1909) · JFM 40.1017.07
[16] Zeipel, H. von: Sur les singularités du problème desn corps Ark. Mat. Astr. Fys.4, No. 32 (1908) · JFM 39.0792.14
[17] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton Univ. Press 1941 · Zbl 0026.02302
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