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December  2008, 1(4): 589-595. doi: 10.3934/dcdss.2008.1.589

On the Dziobek configurations of the restricted $(N+1)$-body problem with equal masses

Eduardo S. G. Leandro 1,

1. 

Depto de Matemática, Univ. Fed. de Pernambuco, Av. Prof. Luiz Freire S/N 50740-540, Recife, PE, Brazil

Received  January 2006 Revised  July 2008 Published  September 2008

In this article we show that the $(N-1)$-dimensional central configurations of the restricted $(N+1)$-body problem with equal masses are symmetrical. As a consequence, we are able to prove finiteness and find upper and lower bounds for the number of central configurations.
Keywords: Central configurations., Celestial mechanics, Restricted $n$-body problem.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Eduardo S. G. Leandro. On the Dziobek configurations of the restricted $(N+1)$-body problem with equal masses. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 589-595. doi: 10.3934/dcdss.2008.1.589
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