### 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 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.

Original language | English |
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Pages (from-to) | 121-138 |

Journal | Fundamenta Mathematicae |

Volume | 157 |

Issue number | 2-3 |

Publication status | Published - 1 Dec 1998 |

### Keywords

- Markov graph
- Periodic point
- Piecewise linear map
- Piecewise smooth map with nowhere vanishing Lipschitz continuous derivative
- Solenoid

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## Cite this

Alsedà, L., López, V. J., & Snoha, L. (1998). All solenoids of piecewise smooth maps are period doubling.

*Fundamenta Mathematicae*,*157*(2-3), 121-138.