All solenoids of piecewise smooth maps are period doubling
Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 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.
Keywords:
Markov graph, periodic point, piecewise smooth map with nowhere vanishing Lipschitz continuous derivative, piecewise linear map, solenoid
@article{10_4064_fm_157_2_3_121_138,
author = {Llu{\'\i}s Alsed\`a and V{\'\i}ctor Jim\'enez L\'opez and L'ubom{\'\i}r Snoha},
title = {All solenoids of piecewise smooth maps are period doubling},
journal = {Fundamenta Mathematicae},
pages = {121--138},
year = {1998},
volume = {157},
number = {2},
doi = {10.4064/fm-157-2-3-121-138},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-121-138/}
}
TY - JOUR AU - Lluís Alsedà AU - Víctor Jiménez López AU - L'ubomír Snoha TI - All solenoids of piecewise smooth maps are period doubling JO - Fundamenta Mathematicae PY - 1998 SP - 121 EP - 138 VL - 157 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-121-138/ DO - 10.4064/fm-157-2-3-121-138 LA - en ID - 10_4064_fm_157_2_3_121_138 ER -
%0 Journal Article %A Lluís Alsedà %A Víctor Jiménez López %A L'ubomír Snoha %T All solenoids of piecewise smooth maps are period doubling %J Fundamenta Mathematicae %D 1998 %P 121-138 %V 157 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-121-138/ %R 10.4064/fm-157-2-3-121-138 %G en %F 10_4064_fm_157_2_3_121_138
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
Cité par Sources :