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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Compactness and Index of Ordinary Central Configurations for
the Curved $N$-Body Problem
Shuqiang Zhu School of Economic Mathematics,
Southwestern University of Finance and Economics,
611130 Chengdu, China
Аннотация:
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.
Ключевые слова:
curved $n$-body problem, ordinary central configurations, geodesic configurations,
Morse index, compactness, relative equilibrium, hyperbolic relative equilibrium.
Поступила в редакцию: 16.09.2020 Принята в печать: 22.01.2021
Образец цитирования:
Shuqiang Zhu, “Compactness and Index of Ordinary Central Configurations for
the Curved $N$-Body Problem”, Regul. Chaotic Dyn., 26:3 (2021), 236–257
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1113 https://www.mathnet.ru/rus/rcd/v26/i3/p236
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