We prove that if (M,\omega) is a connected and compact four-dimensional symplectic manifold, there exist three open sets U_1, U_2, U_3 of {\rm Diff}^1_{\omega}(M) (for the C^1 topology) such that:

1. U_1\cup U_2\cup U_3 is dense in {\rm Diff}^1_{\omega}(M);

2. f\in U_1 if and only if f is Anosov and transitive;

3. f\in U_2 if and only if f is partially hyperbolic; and

4. f\in U_3 if and only if f has a stable completely elliptic periodic point.