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math.DS2020
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…
math.DS2020
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…
math.DS2020★ 3 cited
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…