Gabriel Vigny

activity

20242026

most citedSparsity of postcritically finite maps of

P^{k}

and beyond: A complex analytic approach

4 citations · 4 across the 2 of their papers we have counts for

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5 papers · 1 filter

math.DS2026

Rigidity of the Julia set for HÃ©non-Sibony maps

Gabriel Vigny

Let $f$ and $g$ be two HÃ©non-Sibony maps of $C^{k}$ . We show that if they have the same forward Julia set, then they share a common iterate, thereby extending Lamy's result…

math.DS2025★ 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.DS2025

Quantitative equidistribution of periodic points for rational maps

Thomas Gauthier, Gabriel Vigny

We show that periodic points of period $n$ of a complex rational map of degree $d$ equidistribute towards the equilibrium measure $I^¼_{f}$ of the rational map with a rate of converge…

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.DS2024

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…

Rigidity of the Julia set for HÃ©non-Sibony maps

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

Quantitative equidistribution of periodic points for rational maps

Julia sets and bifurcation loci

The Geometric Dynamical Northcott and Bogomolov Properties

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