Infinitely many periodic orbits for the octahedral 7-body problem

We prove the existence of infinitely many symmetric periodic orbits for a regularized octahedral 7-body problem with six small masses placed at the vertices of an octahedron centered in the seventh mass. The main tools for proving the existence of such periodic orbits is the analytic continuation method together with the symmetry of the problem. © 2008 Birkhäuser Verlag Basel/Switzerland.