Diffeomorphisms approximated by Anosov on the 2-torus and their SBR measures

We consider the $C^{2}$ set of $C^{2}$ diffeomorphisms of the 2-torus $\mathbb{T}^{2}$, provided the conditions that the tangent bundle splits into the directed sum $T\mathbb{T}^{2}=E^{s}\oplus E^{u}$ of $Df$-invariant subbundles $E^{s}$, $E^{u}$ and there is $0<\lambda <1$ such that $\Vert Df|_{E^{s}}\Vert <\lambda$ and $\Vert Df|_{E^{u}}\Vert \ge 1$. Then we prove that the set is the union of Anosov diffeomorphisms and diffeomorphisms approximated by Anosov, and moreover every diffeomorphism approximated by Anosov in the $C^{2}$ set has no SBR measures. This is related to a result of Hu-Young.