Bifurcation of central configuration in the \(2N+1\) body problem
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 \(N \geq 945\).
scientific article; zbMATH DE number 2139802