Repelling periodic points and landing of rays for post-singularly bounded exponential maps  [ Points périodiques répulsifs et atterrissage de rayons pour les fonctions exponentielles avec orbite singulière limitée ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1493-1520.

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.

DOI : https://doi.org/10.5802/aif.2888
Classification : 37F10,  37F20
Mots clés : rigidité, atterrissage de rayons, fonction exponentielle, combinatorique
@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'institut Fourier},
     volume = {64},
     number = {4},
     year = {2014},
     doi = {10.5802/aif.2888},
     zbl = {1323.37029},
     mrnumber = {3329671},
     language = {en},
     url = {www.numdam.org/item/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. http://www.numdam.org/item/AIF_2014__64_4_1493_0/

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