Persistence of Wandering Intervals in Self-Similar Affine Interval   Exchange Transformations
  In this article we prove that given a self-similar interval exchange transformation T, whose associated matrix verifies a quite general algebraic condition, there exists an affine interval exchange transformation with wandering intervals that is semi-conjugated to it. That is, in this context the existence of Denjoy counterexamples occurs very often, generalizing the result of M. Cobo in [C]. 
Xavier Bressaud, Pascal Hubert, Alejandro Maass