T. Gauthier

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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.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…

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

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