All solenoids of piecewise smooth maps are period doubling

Volume 157 / 1998

Lluís Alsedà, Víctor Jiménez López, L'ubomír Snoha Fundamenta Mathematicae 157 (1998), 121-138 DOI: 10.4064/fm-157-2-3-121-138


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.


  • Lluís Alsedà
  • Víctor Jiménez López
  • L'ubomír Snoha

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