Exclusion of Infinite Spin for N-body problem in ${\mathbb{R}}^d$

Abstract

We show that there is no infinite spin at total collisions for $-\hat{I}º$-homogeneous N-body problem in higher dimensional Euclidean space ${\mathbb{R}}^d$, in which $0<\hat{I}º<2$ ($\hat{I}º=1$ the Newtonian case), provided the limiting normalized central configuration is isolated and is of dimension d or d - 1. In the Newtonian case $\hat{I}º=1$, this extends the work of Moeckel-Montgomery to $d\ge 3$ and in the d = 3 case offers a different approach as compared to the current preprint of Pinzari-Zgliczynski.

15 pages