T. Gauthier

activity

20112026

most citedContinuity of the Green function in meromorphic families of polynomials

18 citations · 71 across the 25 of their papers we have counts for

collaborators

31 papers

math.DS2026

Sparsity and uniformity in dynamical Manin--Mumford problems

Thomas Gauthier, Johan Taflin

For endomorphisms of the complex projective plane of a given degree, we prove that the existence of a special curve of bounded degree, in the sense of the dynamical Manin--Mumford…

math.DS2024

Julia sets and bifurcation loci

Thomas Gauthier, Gabriel Vigny

We prove that several dynamically defined fractals in $C$ and $C^{2}$ which arise from different type of polynomial dynamical systems can not be the same objects. O…

math.DS2023

The Geometric Dynamical Northcott Property in the quadratic family

Thomas Gauthier, Gabriel Vigny

The aim of this note is to give a proof of Theorem A from our work on the geometric Northcott property in the simpler case of the quadratic family; being in dimension $1$ in both t…

math.NT2023

Variation of canonical heights of subvarieties for polarized endomorphisms

Thomas Gauthier, Gabriel Vigny

When an endomorphism $f : X \to X$ of a projective variety which is polarized by an ample line bundle $L$ , i.e. such that $f^{*} L ≃ L^{\otimes d}$ with $d \geq 2$ , is defined over a n…

math.DS2023★ 4 cited

Sparsity of postcritically finite maps of $P^{k}$ and beyond: A complex analytic approach

Thomas Gauthier, Johan Taflin, Gabriel Vigny

An endomorphism $f : P^{k} \to P^{k}$ of degree $d \geq 2$ is said to be postcritically finite (or PCF) if its critical set $Crit (f)$ is preperiodic, i.e. if there…

math.DS2023

Complex Dynamics of birational maps of $P^{k}$ defined over a number field

Thomas Gauthier, Gabriel Vigny

Jonsson and Reschke showed that birational selfmaps on projective surface defined over a number field satisfy the energy condition of Bedford and Diller so their ergodic properties…

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.DS2022

When do two rational functions have locally biholomorphic Julia sets?

Romain Dujardin, Charles Favre, Thomas Gauthier

In this article we address the following question, whose interest was recently renewed by problems arising in arithmetic dynamics: under which conditions does there exist a local b…

math.NT2021

Good height functions on quasi-projective varieties: equidistribution and applications in dynamics

Thomas Gauthier

In the present article, we define a notion of good height functions on quasi-projective varieties $V$ defined over number fields and prove an equidistribution theorem of small poin…

math.DS2020

The Geometric Dynamical Northcott Property For Regular Polynomial Automorphisms of the Affine Plane

Thomas Gauthier, Gabriel Vigny

We establish the finiteness of periodic points, that we called Geometric Dynamical Northcott Property, for regular polynomials automorphisms of the affine plane over a function fie…

math.DS2020

The arithmetic of polynomial dynamical pairs

Charles Favre, Thomas Gauthier

We study one-dimensional algebraic families of pairs given by a polynomial with a marked point. We prove an "unlikely intersection" statement for such pairs thereby exhibiting stro…

math.DS2020★ 3 cited

Parametric Lyapunov exponents

Henry De Thélin, Thomas Gauthier, Gabriel Vigny

In an algebraic family of rational maps of $P^{1}$ , we show that, for almost every parameter for the trace of the bifurcation current of a marked critical value, the critica…

math.DS2019★ 11 cited

The Geometric Dynamical Northcott and Bogomolov Properties

Thomas Gauthier, Gabriel Vigny

We establish the dynamical Northcott property for polarized endomorphisms of a projective variety over a function field $K$ of characteristic zero, and we relate this prop…

math.DS2018

Dynamical pairs with an absolutely continuous bifurcation measure

Thomas Gauthier

In this article, we study algebraic dynamical pairs $(f, a)$ parametrized by an irreducible quasi-projective curve $Λ$ having an absolutely continuous bifurcation measure. We prove…

math.DS2018

The bifurcation measure has maximal entropy

Henry De Thélin, Thomas Gauthier, Gabriel Vigny

Let $Λ$ be a complex manifold and let $(f_{λ})_{λ \in Λ}$ be a holomorphic family of rational maps of degree $d \geq 2$ of $P^{1}$ . We define a natural notion of entropy of bifu…

math.DS2018

Approximation of non-archimedean Lyapunov exponents and applications over global fields

Thomas Gauthier, Yusuke Okuyama, Gabriel Vigny

Let $K$ be an algebraically closed field of characteristic 0 that is complete with respect to a non-archimedean absolute value. We establish a locally uniform approximation formula…

math.DS2017★ 18 cited

Continuity of the Green function in meromorphic families of polynomials

Charles Favre, Thomas Gauthier

We prove that along any marked point the Green function of a meromorphic family of polynomials parameterized by the punctured unit disk explodes exponentially fast near the origin…

math.DS2017

Collet, Eckmann and the bifurcation measure

Matthieu Astorg, Thomas Gauthier, Nicolae Mihalache +1

The moduli space $M_{d}$ of degree $d \geq 2$ rational maps can naturally be endowed with a measure $μ_{bif}$ detecting maximal bifurcations, called the bifurcation me…

math.DS2017★ 2 cited

Hyperbolic components of rational maps: Quantitative equidistribution and counting

Thomas Gauthier, Yûsuke Okuyama, Gabriel Vigny

Let $Λ$ be a quasi-projective variety and assume that, either $Λ$ is a subvariety of the moduli space $M_{d}$ of degree $d$ rational maps, or $Λ$ parametrizes an algebraic…

math.DS2016★ 6 cited

Distribution of points with prescribed derivative in polynomial dynamics

Thomas Gauthier, Gabriel Vigny

In analogy to the equidistribution of preimages of a prescribed point by the iterates of a polynomial map in the complex plane towards the equilibrium measure, we show here the equ…

math.DS2016

Classification of special curves in the space of cubic polynomials

Charles Favre, Thomas Gauthier

We describe all special curves in the parameter space of complex cubic polynomials, that is all algebraic irreducible curves containing infinitely many post-critically finite polyn…

math.DS2016★ 5 cited

Symmetrization of Rational Maps: Arithmetic Properties and Families of Lattès Maps of $P^{k}$

Thomas Gauthier, Benjamin Hutz, Scott Kaschner

In this paper we study properties of endomorphisms of $\p^k$ using a symmetric product construction $(\p^1)^k/\mathfrak{S}_k \cong \p^k$. Symmetric products have been used to produ…

math.DS2016

Distribution of postcritically finite polynomials iii: Combinatorial continuity

Thomas Gauthier, Gabriel Vigny

In the first part of the present paper, we continue our study of distribution of postcritically finite parameters in the moduli space of polynomials: we show the equidistribution o…

math.DS2015★ 2 cited

Distribution of postcritically finite polynomials II: Speed of convergence

Thomas Gauthier, Gabriel Vigny

In the moduli space of degree d polynomials, we prove the equidistribution of postcritically finite polynomials toward the bifurcation measure. More precisely, using complex analyt…

Sparsity and uniformity in dynamical Manin--Mumford problems

Julia sets and bifurcation loci

The Geometric Dynamical Northcott Property in the quadratic family

Variation of canonical heights of subvarieties for polarized endomorphisms

Sparsity of postcritically finite maps of Pk and beyond: A complex analytic approach

Complex Dynamics of birational maps of Pk defined over a number field

Entire or rational maps with integer multipliers

When do two rational functions have locally biholomorphic Julia sets?

Good height functions on quasi-projective varieties: equidistribution and applications in dynamics

The Geometric Dynamical Northcott Property For Regular Polynomial Automorphisms of the Affine Plane

The arithmetic of polynomial dynamical pairs

Parametric Lyapunov exponents

The Geometric Dynamical Northcott and Bogomolov Properties

Dynamical pairs with an absolutely continuous bifurcation measure

The bifurcation measure has maximal entropy

Approximation of non-archimedean Lyapunov exponents and applications over global fields

Continuity of the Green function in meromorphic families of polynomials

Collet, Eckmann and the bifurcation measure

Hyperbolic components of rational maps: Quantitative equidistribution and counting

Distribution of points with prescribed derivative in polynomial dynamics

Classification of special curves in the space of cubic polynomials

Symmetrization of Rational Maps: Arithmetic Properties and Families of Lattès Maps of Pk

Distribution of postcritically finite polynomials iii: Combinatorial continuity

Distribution of postcritically finite polynomials II: Speed of convergence

Sparsity of postcritically finite maps of $P^{k}$ and beyond: A complex analytic approach

Complex Dynamics of birational maps of $P^{k}$ defined over a number field

Symmetrization of Rational Maps: Arithmetic Properties and Families of Lattès Maps of $P^{k}$