Bifurcations of Central Configurations in the Four-Body Problem with   some equal masses
  We study the bifurcations of central configurations of the Newtonian four-body problem when some of the masses are equal. First, we continue numerically the solutions for the equal mass case, and we find values of the mass parameter at which the number of solutions changes. Then, using the Krawczyk method and some result of equivariant bifurcation theory, we rigorously prove the existence of such bifurcations and classify them. 
David Rusu, Manuele Santoprete
math-ph math.MP