Generic Finiteness for Dziobek Configurations

Moeckel, Richard

doi:10.1090/S0002-9947-01-02828-8

Generic Finiteness for Dziobek Configurations
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Trans. Amer. Math. Soc. 353 (2001), 4673-4686 Request permission

Abstract:

The goal of this paper is to show that for almost all choices of $n$ masses, $m_i$, there are only finitely many central configurations of the Newtonian $n$-body problem for which the bodies span a space of dimension $n-2$ (such a central configuration is called a Dziobek configuration). The result applies in particular to two-dimensional configurations of four bodies and three-dimensional configurations of five bodies.

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