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              <p>The stability of self-gravitating systems is aborded by the new way of symplectic mechanics. On an analytic way, this energy method allows to simplify a lot of classical results, to open a new investigation method for open problems in this field and to propose new conjectures about the stability of collisionless spherical self-gravitating systems. Some numerical simulation, performed on a connexion machine 5, allows to confirm these conjectures by proposing a new universal stability parameter for collisionless spherical self-gravitating systems.</p>
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              <p>L'etude de la dynamique et de la stabilite des systemes auto-gravitants est abordee sous le jour nouveau de la mecanique symplectique. D'un point de vue analytique une approche de la stabilite par des methodes d'energie permet de simplifier un certain nombre de resultats classiques, de mettre sur pied un schema d'investigation des problemes ouverts dans ce domaine, et de proposer des conjectures sur la stabilite des systemes auto-gravitants non collisionels spheriques. La mise en uvre de simulations numeriques de tels systemes sur une connexion machine permet alors de confirmer ces conjectures en proposant un parametre de stabilite universel des objets auto-gravitants non collisionels spheriques</p>
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