Sur les ensembles de Julia et Fatou des fonctions entières ultramétriques
Annales de l'Institut Fourier, Tome 51 (2001) no. 6, p. 1635-1661
Soit p un nombre premier rationnel. Le sujet de l’article est l’étude de la dynamique des fonctions entières p-adiques. On démontre des résultats analogues à ceux connus dans le domaine complexe, en particulier si deux fonctions entières p-adiques qui ont un point répulsif commun commutent, alors leurs ensembles de Julia et de Fatou sont les mêmes.
Let p a rational prime number. The paper is on the dynamics of p-adic entire functions. We prove results analogous to those known in complex dynamical system. In particular, for commuting entire transcendental functions, under the condition that they have a common periodical repulsive point, they have the same Julia and Fatou sets.
DOI : https://doi.org/10.5802/aif.1869
Classification:  37F99,  11S99
Mots clés: fonctions entières p-adiques, ensemble de Julia, ensemble de Fatou, dynamique p-adique
@article{AIF_2001__51_6_1635_0,
     author = {B\'ezivin, Jean-Paul},
     title = {Sur les ensembles de Julia et Fatou des fonctions enti\`eres ultram\'etriques},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {6},
     year = {2001},
     pages = {1635-1661},
     doi = {10.5802/aif.1869},
     zbl = {01710113},
     mrnumber = {1871284},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2001__51_6_1635_0}
}
Bézivin, Jean-Paul. Sur les ensembles de Julia et Fatou des fonctions entières ultramétriques. Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1635-1661. doi : 10.5802/aif.1869. https://www.numdam.org/item/AIF_2001__51_6_1635_0/

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