Characterization of minimal sequences associated with self-similar interval exchange maps

Abstract

The construction of affine interval exchange maps (IEMs) with wandering intervals that are semi-conjugate to a given self-similar IEM is strongly related to the existence of the so-called minimal sequences associated with local potentials, which are certain elements of the substitution subshift arising from the given IEM. In this article, under the condition called unique representation property, we characterize such minimal sequences for potentials coming from non-real eigenvalues of the substitution matrix. We also give conditions on the slopes of the affine extensions of a self-similar IEM that determine whether it exhibits a wandering interval or not.