# American Institute of Mathematical Sciences

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

 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.
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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