  We consider diffeomorphisms in the $C^\infty$-closure of the conjugancy class
of translations of the 2-torus. By a theorem of Fathi and Herman, a generic
diffeomorphism in that space is minimal and uniquely ergodic. We define a new
mixing-like property, which takes into account the "directions" of mixing, and
we prove that generic elements of the space in question satisfy this property.
As a consequence, we show that there is a residual set of strictly ergodic
diffeomorphisms without invariant foliations of any kind. We also obtain an
analytic version of these results.
