Bifurcation of central configuration in the \(2N+1\) body problem
type: Item
instance of: scholarly article
title: Bifurcation of central configuration in the \(2N+1\) body problem
zbMATH Open document ID: 1138.70008
author: Masayoshi Sekiguchi
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-02-28T00:00:00Z
review text: The author applies bifurcation theory to a special case of Newtonian \((2N+1)\)-body problem (\((2N+1) \geq 7\)) or the so-called rosette configuration. The \(2N\) particles of equal masses \(m\) are at the vertices of two different coplanar and concentric regular \(N\)-gons whose nearest radii span the angle \(\pi/N\). There is an another particle of mass \(m_0\) at the common center of the two \(N\)-gons. Masses in each \(N\)-gon respectively move homothetically. It was known that there exists a bifurcation of central configuration for \(N\geq 3\). Here, by combining the results of the previous studies and a theorem proved in this article, it is concluded that there exists bifurcation of central configuration in the Newtonian \(N\)-body problem for \(N \leq 13\), for any odd number \(N\in [15, 943],\) and for any \(N \geq 945\).
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 2139802
zbMATH Keywords: relative equilibrium
zbMATH Keywords: rosette configuration
MaRDI profile type: Publication
full work available at URL: s10569-004-1991-2
OpenAlex ID: W2053297396
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DOI: 10.1007/S10569-004-1991-2
description: scientific article; zbMATH DE number 2139802