Dynamique des polynômes quadratiques sur les corps locaux
Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 2, pp. 325-336.

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.

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.

Received:
Published online:
DOI: 10.5802/jtnb.589
Robert Benedetto 1; Jean-Yves Briend 2; Hervé Perdry 3

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
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Robert Benedetto; Jean-Yves Briend; Hervé Perdry. Dynamique des polynômes quadratiques sur les corps locaux. Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 2, pp. 325-336. doi : 10.5802/jtnb.589. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.589/

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