7 citations · 9 across the 6 of their papers we have counts for
12 papers
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…
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…
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…
Parametric Lyapunov exponents
Henry De Thélin, Thomas Gauthier, Gabriel Vigny
In an algebraic family of rational maps of , we show that, for almost every parameter for the trace of the bifurcation current of a marked critical value, the critica…
Dynamical pairs with an absolutely continuous bifurcation measure
Thomas Gauthier
In this article, we study algebraic dynamical pairs parametrized by an irreducible quasi-projective curve having an absolutely continuous bifurcation measure. We prove…
The bifurcation measure has maximal entropy
Henry De Thélin, Thomas Gauthier, Gabriel Vigny
Let be a complex manifold and let be a holomorphic family of rational maps of degree of . We define a natural notion of entropy of bifu…