Dynamique des polynômes quadratiques sur les corps locaux

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

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 2, page 325-336
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Benedetto, Robert, Briend, Jean-Yves, and Perdry, Hervé. "Dynamique des polynômes quadratiques sur les corps locaux." Journal de Théorie des Nombres de Bordeaux 19.2 (2007): 325-336. <http://eudml.org/doc/249958>.

@article{Benedetto2007,
abstract = {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.},
affiliation = {Department of Mathematics and Computer Science Amherst College, P. O. Box 5000 Amherst, MA 01002-5000, USA; Université de Provence Laboratoire Analyse, Topologie, Probabilités, UMR CNRS 6632 39 rue Joliot-Curie 13453 Marseille cedex 13, FRANCE; INSERM U535, Université Paris-Sud Pavillon Leriche Secteur Jaune - Porte 18 BP 1000, 94817 Villejuif Cedex, France},
author = {Benedetto, Robert, Briend, Jean-Yves, Perdry, Hervé},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {quadratic polynomials; Julia sets; local fields},
language = {fre},
number = {2},
pages = {325-336},
publisher = {Université Bordeaux 1},
title = {Dynamique des polynômes quadratiques sur les corps locaux},
url = {http://eudml.org/doc/249958},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Benedetto, Robert
AU - Briend, Jean-Yves
AU - Perdry, Hervé
TI - Dynamique des polynômes quadratiques sur les corps locaux
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 2
SP - 325
EP - 336
AB - 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.
LA - fre
KW - quadratic polynomials; Julia sets; local fields
UR - http://eudml.org/doc/249958
ER -

References

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