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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generic property of the bounded syzygy solutions


Author: Florin N. Diacu
Journal: Proc. Amer. Math. Soc. 116 (1992), 809-812
MSC: Primary 70F07
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1123650-1
PII: S 0002-9939(1992)1123650-1
Keywords: $ 3$-body problem, syzygy solution, ergodic theory, Lebesgue measure
Article copyright: © Copyright 1992 American Mathematical Society