Stacked Central Configurations in the 5-Vortex Problem

Fernandes, Antônio Carlos; Vidal, Cláudio

doi:10.1007/s00332-021-09741-1

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2022

2023

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“…The second question has still no answer in R 3 , although it is obvious in R d (d ≥ 4), see Theorem 5 in this paper. Other results about the stacked central configurations are refered in [7,9,10,15,16,[26][27][28]37].…”

Section: Introductionmentioning

confidence: 99%

Stacked central configurations with a homogeneous potential in $\mathbb{R}^3$

Yangshanshan¹,

Zhang²

2022

Preprint

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In this paper we generalize some results in [40] concerning stacked central configurations. We can deal with the general homogeneous potential U α (containing the vortex case) in R 3 . We give the admissible set of α for a convex central configuration (with respect to the Newtonian potential i.e. α = 3). We discuss some properties of the regular n-gon cocircular central configurations. We also find that the stacked property is particular for central configurations by studying the S-balanced configuration case.

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