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Zbl 1175.70013
Lei, J.; Santoprete, M.
Rosette central configurations, degenerate central configurations and bifurcations.
(English)
[J] Celest. Mech. Dyn. Astron. 94, No. 3, 271-287 (2006). ISSN 0923-2958; ISSN 1572-9478/e

Summary: In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another n-gon concentric with the first, but rotated of an angle $\pi /n$, and an additional particle of mass $m_0$ lies at the center of mass of the system. This system admits two mass parameters $\mu = m_0/m_1$ and $\epsilon = m_2/m_1$. We show that, as $\mu$ varies, if $n > 3$, there is a degenerate central configuration and a bifurcation for every $\epsilon > 0$, while if $n = 3$ there is a bifurcation only for some values of $\epsilon$.
MSC 2000:
*70F10 n-body problem

Keywords: bifurcations; central configurations; degenerate central configurations; $n$-body problem

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