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Topological bifurcations of central configurations in the -body problem

2012; Elsevier BV; Volume: 14; Issue: 1 Linguagem: Inglês

10.1016/j.nonrwa.2012.07.027

1878-5719

Ernesto Pérez-Chavela, Sławomir Rybicki,

Advanced Differential Equations and Dynamical Systems

In this article we study topological bifurcations of classes of central configurations of the spatial 6- and 7-body problems. We treat these classes as SO(3)-orbits of critical points of a family of SO(3)-invariant potentials. Using the equivariant bifurcation theory technique, we prove the existence of a global topological bifurcation of classes of central configurations in the 7-body problem and a local topological bifurcation in the 6-body problem.