THE ARITHMETIC OF POLYNOMIAL DYNAMICAL PAIRS

Étude arithmétique des paires dynamiques polynomiales

Charles Favre (1, 2) , Thomas Gauthier (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 UBC - University of British Columbia

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 strong rigidity features for these pairs. We infer from this result the dynamical André-Oort conjecture for curves in the moduli space of polynomials, by describing one-dimensional families in this parameter space containing infinitely many post-critically finite parameters.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]; Variables complexes [math.CV]; Théorie des nombres [math.NT]

Charles Favre, Thomas Gauthier. THE ARITHMETIC OF POLYNOMIAL DYNAMICAL PAIRS. 2020. ⟨hal-02556315⟩