All solenoids of piecewise smooth maps are period doubling
Volume 157 / 1998
Fundamenta Mathematicae 157 (1998), 121-138
DOI: 10.4064/fm-157-2-3-121-138
Abstract
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 $p_1 < ... < p_n$ is a periodic orbit of a continuous map f then there is a union set ${q_1,..., q_{n-1}}$ of some periodic orbits of f such that $p_i < q_i < p_{i+1}$ for any i.
