Shuqiang Zhu

611130 Chengdu, China
School of Economic Mathematics, Southwestern University of Finance and Economics


Zhu S.
For the curved $n$-body problem, we show that the set of ordinary central configurations is away from singular configurations in $\mathbb{H}^3$ with positive momentum of inertia, and away from a subset of singular configurations in $\mathbb{S}^3$. We also show that each of the $n!/2$ geodesic ordinary central configurations for $n$ masses has Morse index $n-2$. Then we get a direct corollary that there are at least $\frac{(3n-4)(n-1)!}{2}$ ordinary central configurations for given $n$ masses if all ordinary central configurations of these masses are nondegenerate.
Keywords: curved $n$-body problem, ordinary central configurations, geodesic configurations, Morse index, compactness, relative equilibrium, hyperbolic relative equilibrium
Citation: Zhu S.,  Compactness and Index of Ordinary Central Configurations for the Curved $N$-Body Problem, Regular and Chaotic Dynamics, 2021, vol. 26, no. 3, pp. 236-257

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