  We study the $u$-Gibbs measures of a certain class of uniformly hyperbolic
skew products on $\mathbb{T}^4$. These systems have a strong unstable and a
weak unstable directions. We show that $C^r$-dense and $C^2$-open in this set
every $u$-Gibbs measure is SRB, in particular, there is only one such measure.
As an application of this, we can obtain the minimality of the strong unstable
foliation.

Dynamical Systems