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 'wild' hyperbolic sets having per
sistent homoclinic tangencies. Furthermore, for a residual subset in an ope
n set of nearby systems, these basic sets are accumulated by periodic ellip
tic islands.