  The construction of affine interval exchange maps with wandering intervals
that are semi-conjugate with a given self-similar interval exchange map is
strongly related with the existence of the so called minimal sequences
associated with local potentials, which are certain elements of the
substitution subshift arising from the given interval exchange map. 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 interval exchange map that determine
whether it exhibits a wandering interval or not.
