[Fractions rationnelles avec multiplicateurs rationnels]
In this article, we show that every rational map whose multipliers all lie in a given number field is a power map, a Chebyshev map or a Lattès map. This strengthens a conjecture by Milnor concerning rational maps with integer multipliers, which was recently proved by Ji and Xie.
Dans cet article, nous montrons que toute fraction rationnelle dont les multiplicateurs sont tous dans un corps de nombres donné est une application puissance, une application de Tchebychev ou un exemple de Lattès. Ceci généralise une conjecture de Milnor concernant les fractions rationnelles avec multiplicateurs entiers, qui a été récemment démontrée par Ji et Xie.
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Keywords: Multiplier spectrum, exceptional maps, arithmetic dynamics
Mots-clés : Multiplicateur, application exceptionnelle, dynamique arithmétique
Huguin, Valentin 1
CC-BY 4.0
@article{JEP_2023__10__591_0,
author = {Huguin, Valentin},
title = {Rational maps with rational multipliers},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {591--599},
year = {2023},
publisher = {Ecole polytechnique},
volume = {10},
doi = {10.5802/jep.227},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jep.227/}
}
TY - JOUR AU - Huguin, Valentin TI - Rational maps with rational multipliers JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 591 EP - 599 VL - 10 PB - Ecole polytechnique UR - https://www.numdam.org/articles/10.5802/jep.227/ DO - 10.5802/jep.227 LA - en ID - JEP_2023__10__591_0 ER -
Huguin, Valentin. Rational maps with rational multipliers. Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 591-599. doi: 10.5802/jep.227
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