All solenoids of piecewise smooth maps are period doubling

We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if p1 < ... < pn is a periodic orbit of a continuous map f then there is a union set {q1,..., qn-1} of some periodic orbits of f such that Pi < qi < Pi+i for any i.