Distribution of postcritically finite polynomials III: Combinatorial continuity

Thomas Gauthier, Gabriel Vigny
2019 Fundamenta Mathematicae  
In the first part of the present paper, we continue our study of the distribution of postcritically finite parameters in the moduli space of polynomials: we show the equidistribution of Misiurewicz and parabolic parameters with prescribed combinatorics toward the bifurcation measure. Our results essentially rely on a combinatorial description of the escape locus and of the bifurcation measure developped by Kiwi and Dujardin-Favre. In the second part of the paper, we construct a bifurcation
more » ... a bifurcation measure for the connectedness locus of the quadratic anti-holomorphic family which is supported by a strict subset of the boundary of the Tricorn. We also establish an approximation property by Misiurewicz parameters in the spirit of the previous one. Finally, we answer a question of Kiwi, exhibiting in the moduli space of degree 4 polynomials, non-trivial Impression of specific combinatorics.
doi:10.4064/fm220-2-2018 fatcat:razwz62wcbhnziy6dsc3ppkt4q