Niding designs of models of constant inclination for generalized shifts of a segment

For one-dimensional discontinuous maps with zero topological entropy we apply the technique of kneading invariants and kneading series. The kneading technique was introduced first by J. Milnor and W. Thurston for continuous piecewise monotonic one-dimensional maps and was applied to maps with positive topological entropy. In the present paper we show that by approaching the zero entropy one using kneading series may define invariant measure for generalized interval exchange transformations and also for a class of discontinuous maps without periodic points. Thus, in terms of kneading series we construct a semiconjugacy (being actually a conjugacy in the transitive case) with a model map of unit (in absolute value) slope. The proposed construction is determined by formulas which allow to calculate the parameters of the model map with required accuracy.