Compactness and index of ordinary central configurations for the curved n-body problem
Dynamical Systems
2021-06-16 v2
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.
Keywords
Cite
@article{arxiv.2003.06850,
title = {Compactness and index of ordinary central configurations for the curved n-body problem},
author = {Shuqiang Zhu},
journal= {arXiv preprint arXiv:2003.06850},
year = {2021}
}
Comments
30 pages, 1 figure