Gabriel Vigny

activity

20242026

collaborators

4 papers

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

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