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

Xiang Yu; Lei Zhao

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arXiv · 2606.31196

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

Xiang Yu·Lei Zhao

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Abstract

We show that there is no infinite spin at total collisions for $-\kappa$-homogeneous N-body problem in higher dimensional Euclidean space $\mathbb{R}^d$, in which $0 < \kappa < 2$ ($\kappa = 1$ the Newtonian case), provided the limiting normalized central configuration is isolated and is of dimension d or d - 1. In the Newtonian case $\kappa = 1$, 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.

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Xiang Yu, Lei Zhao. 2026-06-30. Exclusion of Infinite Spin for N-body problem in $\mathbb{R}^d$. https://arxiv.org/abs/2606.31196

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