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Algebraic structure of the manifold of solutions of the $ N$-body problem


Author: Lawrence Goldman
Journal: Proc. Amer. Math. Soc. 25 (1970), 417-422
MSC: Primary 12.80; Secondary 70.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0260714-4
MathSciNet review: 0260714
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Abstract: The Theorem of Ritt on the decomposition of the perfect differential ideal generated by a single irreducible differential polynomial is, here, generalized to system of polynomials satisfying certain conditions. We use these results to prove that all solutions of the $ N$-body problem, excepting the solutions for which one or more of the $ {r_{ij}}$ (the distance between the masses $ {M_i},\;{M_j}$) is zero, belong to one irreducible manifold.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0260714-4
Keywords: Manifold of systems, decomposition of radical ideals, decomposition of perfect differential ideals, Jacobian, $ N$-body problem, three-body problem
Article copyright: © Copyright 1970 American Mathematical Society