[Points périodiques répulsifs et atterrissage de rayons pour les fonctions exponentielles avec orbite singulière limitée]
On montre que, pour toute fonction exponentielle avec orbite singulière bornée, chaque point périodique répulsif est le point d’atterrissage d’au moins un rayon externe avec adresse périodique. Cela généralise un théorème de Douady qui s’applique au polynômes complexes avec ensemble de Julia connexe, dont on donne une nouvelle démonstration.
We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this allows us to conclude that the singular value itself is accessible.
Keywords: rigidity, accessibility, exponential maps, combinatorics
Mot clés : rigidité, atterrissage de rayons, fonction exponentielle, combinatorique
Benini, Anna Miriam 1 ; Lyubich, Mikhail 2
@article{AIF_2014__64_4_1493_0,
author = {Benini, Anna Miriam and Lyubich, Mikhail},
title = {Repelling periodic points and landing of rays for post-singularly bounded exponential maps},
journal = {Annales de l'Institut Fourier},
pages = {1493--1520},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {64},
number = {4},
year = {2014},
doi = {10.5802/aif.2888},
zbl = {1323.37029},
mrnumber = {3329671},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2888/}
}
TY - JOUR AU - Benini, Anna Miriam AU - Lyubich, Mikhail TI - Repelling periodic points and landing of rays for post-singularly bounded exponential maps JO - Annales de l'Institut Fourier PY - 2014 SP - 1493 EP - 1520 VL - 64 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2888/ DO - 10.5802/aif.2888 LA - en ID - AIF_2014__64_4_1493_0 ER -
%0 Journal Article %A Benini, Anna Miriam %A Lyubich, Mikhail %T Repelling periodic points and landing of rays for post-singularly bounded exponential maps %J Annales de l'Institut Fourier %D 2014 %P 1493-1520 %V 64 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2888/ %R 10.5802/aif.2888 %G en %F AIF_2014__64_4_1493_0
Benini, Anna Miriam; Lyubich, Mikhail. Repelling periodic points and landing of rays for post-singularly bounded exponential maps. Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1493-1520. doi : 10.5802/aif.2888. https://aif.centre-mersenne.org/articles/10.5802/aif.2888/
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