Thomas Gauthier

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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

HÃ¶lder estimates and uniformity in arithmetic dynamics

Thomas Gauthier

In this note we study common preperiodic points of rational maps of the Riemann Sphere. We show that given any degrees $d_{1}, d_{2} \geq 2$ , outside a Zariski closed subset of the space…