Stable accessibility is C1 dense

We prove that in the space of all Cr (r 1) partially hyperbolic dieomorphisms, there is a C1 open and dense set of accessible dif-feomorphisms. This settles the C1 case of a conjecture of Pugh and Shub. The same result holds in the space of volume preserving or symplectic partially hyperbolic dieomorphisms. Combining this theorem with results in [Br], [Ar] and [PugSh3], we obtain several corollaries. The rst states that in the space of volume preserving or symplectic partially hyperbolic dieomorphisms, topological transitivity holds on an open and dense set. Further, on a symplectic n-manifold (n 4) the C1-closure of the stably transitive symplectomorphisms is precisely the closure of the partially hyperbolic symplectomorphisms. Finally, stable ergodicity is C 1 open and dense among the volume preserving, partially hyperbolic dieomorphisms satisfying the additional technical hypotheses of [PugSh3]