CENTRAL CONFIGURATIONS WITH MANY SMALL MASSES

By using the method of analytical continuation, we find the exact numbers of central configurations for some open sets of n positive masses for any choice of n. It turns out that the numbers increase dramatically as n increases; e.g., for some open set of 18 positive masses, some 2.08766 × 1020 classes of distinctive central configurations are found. In the mean time, we obtained some results about the Hausdorff measure for the set of n positive masses where degenerate central configuration arises. © 1991.