JournalscmhVol. 80, No. 3pp. 593–629

Points périodiques des fonctions rationnelles dans l'espace hyperbolique pp-adique

  • Juan Rivera-Letelier

    Pontifica Universidad Católica de Chile, Santiago, Chile
Points périodiques des fonctions rationnelles dans l'espace hyperbolique $p$-adique cover
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Abstract

We study the dynamics of rational maps with coefficients in the field Cp{\Bbb C}_p acting on the hyperbolic space Hp{\Bbb H}_p. Our main result is that the number of periodic points in Hp{\Bbb H}_p of such a rational map is either 00, 11 or \infty, and we characterize those rational maps having precisely 00 or 11 periodic points. The main property we obtain is a criterion for the existence of infinitely many periodic points (of a special kind) in hyperbolic space. The proof of this criterion is analogous to G. Julia's proof of the density of repelling periodic points in the Julia set of a complex rational map.

Cite this article

Juan Rivera-Letelier, Points périodiques des fonctions rationnelles dans l'espace hyperbolique pp-adique. Comment. Math. Helv. 80 (2005), no. 3, pp. 593–629

DOI 10.4171/CMH/27