Classification of all planar central configurations of N bodies with equal masses in the case of the logarithmic potential and N < 8
Résumé
First we give a new way to model the problem using complex numbers and elementary symetric functions. The new equations can be solved by hand for N=4 and several infinite families can be found using this new formulation. By using Groebner bases computations we are able to make a complete classification of the solutions for N=4,5,6,7. For N < 8 there is a always a finite number of solutions and a symmetry.