Sur les ensembles de Julia et Fatou des fonctions entières ultramétriques
[On the Julia and Fatou sets of ultrametric entire functions]
Annales de l'Institut Fourier, Volume 51 (2001) no. 6, pp. 1635-1661.

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.

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.

DOI: 10.5802/aif.1869
Classification: 37F99, 11S99
Mot clés : fonctions entières $p$-adiques, ensemble de Julia, ensemble de Fatou, dynamique $p$-adique
Keywords: entire $p$-adic functions, Julia set, Fatou set, ultrametric dynamics
Bézivin, Jean-Paul 1

1 Université de Caen, Département de Mathématiques et Mécanique, Campus II, Boulevard du Maréchal Juin, BP 5186, 14032 Caen Cedex (France)
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Bézivin, Jean-Paul. Sur les ensembles de Julia et Fatou des fonctions entières ultramétriques. Annales de l'Institut Fourier, Volume 51 (2001) no. 6, pp. 1635-1661. doi : 10.5802/aif.1869. https://aif.centre-mersenne.org/articles/10.5802/aif.1869/

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