Inverse problem and Bertrand's theorem
  The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem. 
Yves Grandati (LPMC - EA 3468), Alain B\'erard (LPMC - EA 3468),   Ferhat Menas (LPCQ)