On the spatial central configurations of the 5--body problem andtheir bifurcations

Martha Alvarez; Joaquin Delgado; Jaume Llibre

doi:10.3934/dcdss.2008.1.505

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2008, Volume 1, Issue 4: 505-518. Doi: 10.3934/dcdss.2008.1.505

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On the spatial central configurations of the 5--body problem and their bifurcations

1.
Departamento de Matemáticas, UAM–Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, México, D.F. 09340
2.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

Received: December 31, 2005

Revised: July 31, 2008

Published: November 2008

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Abstract

Central configurations provide special solutions of the general $n$--body problem. Using the mutual distances between the $n$ bodies as coordinates we study the bifurcations of the spatial central configurations of the $5$--body problem going from the problem with equals masses to the $1+4$-- body problem which has one large mass and four infinitesimal equal masses. This study is made by giving a computer--aided proof.

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Mathematics Subject Classification: Primary: 70F15, 70F10; Secondary: 37M20.

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