G. Gabor, M. Quincampoix

Titre: "On attainability of a set by at least one solution to a differential inclusion."

Résumé: In many dynamical systems problems, it is interesting to know not only that an equilibria do exist but also to know if the equilibria can be reached by at least one trajectory (possibly asymptotically). It is worth pointing out that this question is different from those of stability, or attractiveness of the equilibria. In the present paper, our purpose is to give sufficient conditions for answering positively to the above question. More generally we address the question of attainability of a closed set E by at least one trajectory starting from outside E. Our method is based on a kind of Lyapunov Analysis based on Viability Theory and topological methods.