Symplectic C-1-diffeomorphisms of 4-dimensional manifolds

We prove that if (M,omega) is a connected 4-dimensional symplectic manifold , there exists three open sets U-1, U-2, U-3 of Diff(omega)(1) (M) (for the C-1-topology) such that: U-1 boolean OR U-2 boolean OR U-3 is dense in Diff(omega)(1) (M); f is an element of U-1 if and only if f is Anosov and transitive; f is an element of U-2 if and only if f is partially hyperbolic; f is an element of U-3 if and only if f has a stable completely elliptic pe riodic point. (C) 2000 Academie des sciences/Editions scientifiques et medi cales Elsevier SAS.