Topological bifurcations of spatial central configurations in the N-body problem

Abstract

We study topological bifurcations of classes of spatial central configurations (s.c.c.) from the following highly symmetrical families: two nested regular tetrahedra, octahedra and cubes, two nested rotated regular tetrahedra and two dual regular polyhedra for 14 bodies. We prove the existence of local and global topological bifurcations of s.c.c. from these families. We seek new classes of s.c.c. by using equivariant bifurcation theory. It is worth pointing out that the shapes of the bifurcating families are less symmetrical than the shapes of the considered families of s.c.c.