Valentin Huguin

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20192026

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5 papers · 1 filter

math.DS2026

An arithmetic approach to parabolic multiplicity in complex dynamics

Xavier Buff, Valentin Huguin, Liz Vivas

When $ω$ is a primitive $n$ -th root of unity, the quadratic polynomial $F (z) = ω z (1 - z)$ and the entire map $F (z) = ω z e^{- z}$ both have a parabolic fixed point at $0$ . T…

math.DS2024

Moduli spaces of polynomial maps and multipliers at small cycles

Valentin Huguin

Fix an integer $d \geq 2$ . The space $P_{d}$ of polynomial maps of degree $d$ modulo conjugation by affine transformations is naturally an affine variety over $\mathbb{Q}…

math.DS2023

Entire maps with rational preperiodic points and multipliers

Xavier Buff, Igors Gorbovickis, Valentin Huguin

Given a number field $K \subset C$ that is not contained in $R$ , we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \m…

math.DS2022

Entire or rational maps with integer multipliers

Xavier Buff, Thomas Gauthier, Valentin Huguin +1

Let $O_{K}$ be the ring of integers of an imaginary quadratic field $K$ . Recently, Ji and Xie proved that every rational map $f \colon \widehat{\mathbb{C}} \rightarrow \w…

math.DS2019

Simultaneously preperiodic integers for quadratic polynomials

Valentin Huguin

In this article, we study the set of parameters $c \in C$ for which two given complex numbers $a$ and $b$ are simultaneously preperiodic for the quadratic polynomial $f_{c…