Abstract
We show that within a C^{1} -neighborhood {\mathcal{U}} of the set of volume preserving Anosov diffeomorphisms on the three-torus {\mathbb{T}^3} which are strongly partially hyperbolic with expanding center, any f\in{\mathcal{U}}\cap{\operatorname{Diff}^2(\mathbb{T}^3)} satisfies the dichotomy: either the strong-stable and strong-unstable bundles E^{s} , E^{u} of f are jointly integrable, or any fully supported u -Gibbs measure of f is SRB.
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