Thursday, June 6, 2013

1306.1047 (Yu Xiang et al.)

Saari's Conjecture and Variational Minimal Solutions for $N$-Body

Yu Xiang, Zhang Shiqing
In this paper, we will prove Saari's conjecture in a particular case by using a arithmetic fact, and then, apply it to prove that for any given positive masses, the variational minimal solutions of the N-body problem in ${\mathbb{R}}^2$ are precisely a relative equilibrium solution whose configuration minimizes the function $IU^2$ in ${{\mathbb{R}}}^2$.
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