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arXiv · 2003.06850

Compactness and index of ordinary central configurations for the curved n-body problem

Shuqiang Zhu
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Abstract

For the curved n-body problem, we show that the set of ordinary central configurations is away from most singular configurations in H^3, and away from a subset of singular configurations in 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 (3n-4)(n-1)!/2 ordinary central configurations for given n masses if all ordinary central configurations of these masses are non-degenerate.

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Shuqiang Zhu. 2020-03-15. Compactness and index of ordinary central configurations for the curved n-body problem. https://doi.org/10.1134/s1560354721030035

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