Christian Bonatti (CNRS und Université de Bourgogne, Dijon, FRANKREICH) Title :"Towards a global view of dynamical systems, for the C1-topology". Abstract: In the beginning of the sixties, it appeared clearly that chaotic dynamical systems could be important for many scientific fields. At the same time, the hyperbolic theory of Anosov Smale presents a large class of chaotic dynamics which could be completely described and understood. However, it is known from the last 60ties that there are open set of non-hyperbolic dynamical systems : each of this system present fragil behavior, so that there is no hope of a complete classification. Results of many dynamicists in the last 10 years suggest a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits the space Diff^1(M) in disjoint open regions whose union is C1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of --either a robust local phenomenon --or a global structure forbidding this local phenomenon. Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.