Uniqueness of $u$-Gibbs measures for hyperbolic skew products on $\mathbb{T}^4$

Abstract

We study the u-Gibbs measures of a certain class of uniformly hyperbolic skew products on 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.