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 y est conjugué au décalage unilatéral sur symboles.
Published online:
DOI: 10.5802/jtnb.589
Author's affiliations:
@article{JTNB_2007__19_2_325_0,
author = {Robert Benedetto and Jean-Yves Briend and Herv\'e Perdry},
title = {Dynamique des polyn\^omes quadratiques sur les corps locaux},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {325--336},
publisher = {Universit\'e Bordeaux 1},
volume = {19},
number = {2},
year = {2007},
doi = {10.5802/jtnb.589},
zbl = {pre05302777},
mrnumber = {2394889},
language = {fr},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.589/}
}
TY - JOUR TI - Dynamique des polynômes quadratiques sur les corps locaux JO - Journal de Théorie des Nombres de Bordeaux PY - 2007 DA - 2007/// SP - 325 EP - 336 VL - 19 IS - 2 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.589/ UR - https://zbmath.org/?q=an%3Apre05302777 UR - https://www.ams.org/mathscinet-getitem?mr=2394889 UR - https://doi.org/10.5802/jtnb.589 DO - 10.5802/jtnb.589 LA - fr ID - JTNB_2007__19_2_325_0 ER -
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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