  The focusing critical wave equation in three dimensions exhibits a special
class of static solutions which are linearly unstable. These solutions decay
like an inverse first power. We construct small codimension one stable
manifolds in the class of radial perturbations for these static solutions. We
show that initial data on this manifold lead to global solutions. Moreover, the
long-time behavior of these solutions can be described explicitly. In
particular, the family of static solutions acts as an attractor for these
solutions. On a technical level, we remark that the linearized operator
exhibits a zero energy resonance, and we develop the tools needed for that
case.
