Rational maps with rational multipliers
Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 591-599.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.227
Classification: 37P35, 37F10, 37P05
Keywords: Multiplier spectrum, exceptional maps, arithmetic dynamics
Mot clés : Multiplicateur, application exceptionnelle, dynamique arithmétique

Valentin Huguin 1

1 Constructor University Bremen gGmbH Campus Ring 1, 28759 Bremen, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Valentin Huguin. Rational maps with rational multipliers. Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 591-599. doi : 10.5802/jep.227. https://jep.centre-mersenne.org/articles/10.5802/jep.227/

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