On the preservation of combinatorial types for maps on trees
Annales de l'Institut Fourier, Volume 55 (2005) no. 7, p. 2375-2398
We study the preservation of the periodic orbits of an A-monotone tree map f:T⟶T in the class of all tree maps g:S⟶S 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.
On étudie la préservation des orbites périodiques des applications A-monotones sur les arbres f:T⟶T, dans la classe de toutes les applications continues sur les arbres g:S⟶S 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.
DOI : https://doi.org/10.5802/aif.2164
Classification:  37E25
Keywords: Tree maps, minimal dynamics
Keywords: Tree maps, minimal dynamics 
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {7},
     year = {2005},
     pages = {2375-2398},
     doi = {10.5802/aif.2164},
     zbl = {1085.37035},
     mrnumber = {2207387},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 55 (2005) no. 7, pp. 2375-2398. doi : 10.5802/aif.2164. http://www.numdam.org/item/AIF_2005__55_7_2375_0/

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