Repelling periodic points and landing of rays for post-singularly bounded exponential maps
Annales de l'Institut Fourier, Volume 64 (2014) no. 4, p. 1493-1520

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.

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.

DOI : https://doi.org/10.5802/aif.2888
Classification:  37F10,  37F20
Keywords: rigidity, accessibility, exponential maps, combinatorics
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {4},
     year = {2014},
     pages = {1493-1520},
     doi = {10.5802/aif.2888},
     zbl = {1323.37029},
     mrnumber = {3329671},
     zbl = {06387315},
     language = {en},
     url = {http://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, Volume 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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