  Consider a generic one-parameter unfolding of a homoclinic tangency of an
area preserving surface diffeomorphism. We show that for many parameters
(residual subset in an open set approaching the critical value) the
corresponding diffeomorphism has a transitive invariant set $\Omega$ of full
Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets
and is accumulated by elliptic islands.
  As an application we prove that stochastic sea of the standard map has full
Hausdorff dimension for sufficiently large topologically generic parameters.
