Dynamique des polynômes quadratiques sur les corps locaux

Benedetto, Robert¹ ; Briend, Jean-Yves² ; Perdry, Hervé³ 

¹ Department of Mathematics and Computer Science Amherst College, P. O. Box 5000 Amherst, MA 01002-5000, USA
² Université de Provence Laboratoire Analyse, Topologie, Probabilités, UMR CNRS 6632 39 rue Joliot-Curie 13453 Marseille cedex 13, FRANCE
³ INSERM U535, Université Paris-Sud Pavillon Leriche Secteur Jaune - Porte 18 BP 1000, 94817 Villejuif Cedex, France

Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 325-336.

Résumé (VO)

Dans cette note, nous montrons que la dynamique d’un polynôme quadratique sur un corps local peut être déterminée en temps fini, et que l’on a l’alternative suivante : soit l’ensemble de Julia est vide, soit $P$ y est conjugué au décalage unilatéral sur $2$ symboles.

Abstract

We show that the dynamics of a quadratic polynomial over a local field can be completely decided in a finite amount of time, with the following two possibilities : either the Julia set is empty, or the polynomial is topologically conjugate on its Julia set to the one-sided shift on two symbols.

Détail

DOI : 10.5802/jtnb.589

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