Geodesic
All solenoids of piecewise smooth maps are period doubling
Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 121-138.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-157-2-3-121-138
Keywords: Markov graph, periodic point, piecewise smooth map with nowhere vanishing Lipschitz continuous derivative, piecewise linear map, solenoid

Lluís Alsedà 1 ; Víctor Jiménez López 1 ; L'ubomír Snoha 1

1 
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Lluís Alsedà; Víctor Jiménez López; L'ubomír  Snoha. All solenoids of piecewise smooth maps are period doubling. Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 121-138. doi : 10.4064/fm-157-2-3-121-138. http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-121-138/

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