ON THE STABILITY OF THE TROJAN ASTEROIDS

We reconsider the problem of stability of the triangular Lagrangian eq uilibria of the restricted problem of three bodies. We consider in par ticular the Sun-Jupiter model and the Trojan asteroids in the neighbou rhood of the point L(4). In the spirit of Nekhoroshev's theory on stab ility over exponentially large times? we are able to prove that stabil ity over the age of the universe is guaranteed on a region big enough to include a few known asteroids. This significantly improves previous works on the same subject.