Abundance of elliptic isles at conservative bifurcations

We prove a conservative analogue of a theorem of Newhouse on the abundance of wild hyperbolic sets: arbitrarily close to any area preserving map with a homoclinic tangency there are maps with ʹwildʹ hyperbolic sets having persistent homoclinic tangencies. Furthermore, for a residual subset in an open set of nearby systems, these basic sets are accumulated by periodic elliptic islands.