Distribution of postcritically finite polynomials

Charles Favre (1) , Thomas Gauthier (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We prove that Misiurewicz parameters with prescribed combinatorics and hyperbolic parameters with (d − 1) distinct attracting cycles with given multipliers are equidistributed with respect to the bifurcation measure in the moduli space of degree d complex polynomials. Our proof relies on Yuan's equidistribution results of points of small heights, and uses in a crucial way Epstein's transversality results.

Mots clés: bifurcation measure; equidistribution; hyperbolic center; points of small height; transversality

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

Charles Favre, Thomas Gauthier. Distribution of postcritically finite polynomials. Israel Journal of Mathematics, 2015, ⟨10.1007/s11856-015-1218-0⟩. ⟨hal-00784620⟩