In this paper we study non-compact extensions of toral translations. We prove that the generic higher dimensional cylindrical cascade (i.e, a skew product in $ \mathbb{T}^d \times \mathbb{R}^{r} $) above a Liouvillian irrational translation is ergodic. Since Liouvillian vectors form a residual set, as a corollary we show that ergodicity is a generic property in the set of skew products over rigid rotations.
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