[Sur la présentation des types combinatoires pour les applications sur les arbres]
On étudie la préservation des orbites périodiques des applications -monotones sur les arbres , dans la classe de toutes les applications continues sur les arbres qui ont un cycle avec le même type d’orbite que . On démontre l’existence d’une application injective de l’ensemble de (presque toutes) les orbites périodiques de dans l’ensemble des orbites périodiques de chaque application dans la classe, préservant la période. De plus, la position relative des orbites correspondantes dans les arbres et (qui ne sont pas forcément homéomorphes) sont essentiellement les mêmes.
We study the preservation of the periodic orbits of an -monotone tree map in the class of all tree maps having a cycle with the same pattern as . We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees and (which need not be homeomorphic) are essentially preserved.
Keywords: Tree maps, minimal dynamics, Tree maps, minimal dynamics
Mot clés : applications sur les arbres, dynamique minimale
@article{AIF_2005__55_7_2375_0,
author = {Alsed\`a, Llu{\'\i}s and Juher, David and Mumbr\'u, Pere},
title = {On the preservation of combinatorial types for maps on trees},
journal = {Annales de l'Institut Fourier},
pages = {2375--2398},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {55},
number = {7},
year = {2005},
doi = {10.5802/aif.2164},
mrnumber = {2207387},
zbl = {1085.37035},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2164/}
}
TY - JOUR AU - Alsedà, Lluís AU - Juher, David AU - Mumbrú, Pere TI - On the preservation of combinatorial types for maps on trees JO - Annales de l'Institut Fourier PY - 2005 SP - 2375 EP - 2398 VL - 55 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2164/ DO - 10.5802/aif.2164 LA - en ID - AIF_2005__55_7_2375_0 ER -
%0 Journal Article %A Alsedà, Lluís %A Juher, David %A Mumbrú, Pere %T On the preservation of combinatorial types for maps on trees %J Annales de l'Institut Fourier %D 2005 %P 2375-2398 %V 55 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2164/ %R 10.5802/aif.2164 %G en %F AIF_2005__55_7_2375_0
Alsedà, Lluís; Juher, David; Mumbrú, Pere. On the preservation of combinatorial types for maps on trees. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2375-2398. doi : 10.5802/aif.2164. http://www.numdam.org/articles/10.5802/aif.2164/
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