Bézivin, Jean-Paul
Sur les ensembles de Julia et Fatou des fonctions entières ultramétriques
Annales de l'institut Fourier, Tome 51 (2001) no. 6 , p. 1635-1661
Zbl 01710113 | MR 1871284
doi : 10.5802/aif.1869
URL stable : http://www.numdam.org/item?id=AIF_2001__51_6_1635_0

Classification:  37F99,  11S99
Mots clés: fonctions entières p-adiques, ensemble de Julia, ensemble de Fatou, dynamique p-adique
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.

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