On the preservation of combinatorial types for maps on trees
[Sur la présentation des types combinatoires pour les applications sur les arbres]
Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2375-2398.

On étudie la préservation des orbites périodiques des applications A-monotones sur les arbres f:TT, dans la classe de toutes les applications continues sur les arbres g:SS qui ont un cycle avec le même type d’orbite que A. On démontre l’existence d’une application injective de l’ensemble de (presque toutes) les orbites périodiques de f 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 T et S (qui ne sont pas forcément homéomorphes) sont essentiellement les mêmes.

We study the preservation of the periodic orbits of an A-monotone tree map f:TT in the class of all tree maps g:SS having a cycle with the same pattern as A. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of f into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved.

DOI : 10.5802/aif.2164
Classification : 37E25
Keywords: Tree maps, minimal dynamics, Tree maps, minimal dynamics
Mot clés : applications sur les arbres, dynamique minimale
Alsedà, Lluís 1 ; Juher, David 2 ; Mumbrú, Pere 3

1 Universitat Autònoma de Barcelona, Departament de Matemàtiques, Edifici Cc,08913 Cerdanyola del Vallès, Barcelona (Espagne)
2 Universitat de Girona, Departament d'Informàtica i Matemàtica Aplicada, Lluís Santaló s/n, 17071 Girona (Espagne)
3 Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08071 Barcelona (Espagne)
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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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