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We give conditions for minimality of $\mathbb Z/N\mathbb Z$ extensions of arotation of angle $\alpha$ with one marked point, solving the problem for anyprime $N$: for $N=2$, these correspond to the Veech 1969 examples, for which anecessary and sufficient condition was not known yet. We provide also a wordcombinatorial criterion of minimality valid for general interval exchangetransformations, which applies to $\mathbb Z/N\mathbb Z$ extensions of anyinterval exchange transformation with any number of marked points. Then we givea condition for unique ergodicity of these extensions when the initial intervalexchange transformation is linearly recurrent and there are one or two markedpoints.

Minimality and unique ergodicity of Veech 1969 type interval exchange transformations