Rational maps with rational multipliers

2022/10/31 by Valentin Huguin, Huguin, Valentin · 1 citation
Mathematics · #37P05 (Secondary) #37P35 (Primary) 37F10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2210.17521

openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• On the centralizers of endomorphisms of the projective line

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