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A generic property of the bounded syzygy solutions


Author: Florin N. Diacu
Journal: Proc. Amer. Math. Soc. 116 (1992), 809-812
MSC: Primary 70F07
DOI: https://doi.org/10.1090/S0002-9939-1992-1123650-1
MathSciNet review: 1123650
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Abstract: For a set of masses having positive measure, excepting eventually a negligible set of initial conditions, every noncollinear bounded solution of the planar three-body problem that has a syzygy configuration encounters an infinity of such configurations. Along a noncollinear syzygy solution, the set of syzygy configuration instants is discrete.


References [Enhancements On Off] (What's this?)

  • [A] V. I. Arnol'd, The classical theory of perturbations and the problem of stability of planetary systems, Soviet Math. Dokl. 3 (1962), 1008-1012.
  • [D] F. N. Diacu, On the planar Syzygy solutions of the $ 3$-body problem, Celestial Mech. 46 (1989), 119-128. MR 1044420 (91b:70019)
  • [M] J. K. Moser, Stable and random motions in dynamical systems, Princeton Univ. Press, Princeton, NJ, 1971.
  • [P] P. Painlevé, Leçons sur la théorie analytiques des equations différentielles, Hermann, Paris, 1897.
  • [S] D. G. Saari, Imporbability of collisions in newtonian gravitational systems, Trans. Amer. Math. Soc. 162 (1971), 267-271; 168 (1972), 521; 181 (1973), 351-368. MR 0295648 (45:4714)
  • [SA] K. L. Samarov, Regularization of the isosceles three-body problem for a nonzero area vector, Soviet Math. Dokl. 18 (1977), 245-249.
  • [SM] C. L. Siegel and J. K. Moser, Lectures on celestial mechanics, Springer-Verlag, Berlin, Heidelberg, and New York, 1971. MR 0502448 (58:19464)
  • [Si] K. A. Sitnikov, The existence of oscillary motion in the three-body problem, Soviet Phys. Dokl. 5 (1961), 647-650. MR 0127389 (23:B435)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1123650-1
Keywords: $ 3$-body problem, syzygy solution, ergodic theory, Lebesgue measure
Article copyright: © Copyright 1992 American Mathematical Society

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