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December  2008, 1(4): 505-518. doi: 10.3934/dcdss.2008.1.505

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

Martha Alvarez 1, , Joaquin Delgado 1, and  Jaume Llibre 2,

1. 

Departamento de Matemáticas, UAM–Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, México, D.F. 09340, Mexico, Mexico
2. 

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

Received  January 2006 Revised  August 2008 Published  September 2008

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.
Keywords: Central configurations, bifurcation., $5$--body problem.
Mathematics Subject Classification: Primary: 70F15, 70F10; Secondary: 37M2.
Citation: Martha Alvarez, Joaquin Delgado, Jaume Llibre. On the spatial central configurations of the 5--body problem and their bifurcations. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 505-518. doi: 10.3934/dcdss.2008.1.505
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