On Stochastic Sea of the Standard Map

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 a stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.