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

Eduardo S. G. Leandro

doi:10.3934/dcdss.2008.1.589

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2008, Volume 1, Issue 4: 589-595. Doi: 10.3934/dcdss.2008.1.589

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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

Received: December 31, 2005

Revised: June 30, 2008

Published: November 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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