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Renato Iturriaga and Ezequiel Maderna (2015)

Generic uniqueness of the minimal Moulton central configuration

Celest. Mech. Dyn. Astron., 123(3):351-361.

We prove that, for generic (open and dense) values of the masses, the Newtonian potential function of the collinear N-body problem has N!/2 critical values when restricted to a fixed inertia level. In particular, we provee that for generic masses, there is only one minimal Moulton configuration. We give a very short proof of an improved version of classical Moulton's theorem using the Gershgorin circle theorem and a normalization of central configurations introduced by Yoccoz in 1986. Then the proof of the main theorem follows by reduction to the case of three bodies, in which we apply a theorem by Euler of 1765.
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