Distribution of postcritically finite polynomials iii: Combinatorial continuity
Abstract
In the first part of the present paper, we continue our study of distribution of postcritically finite parameters in the moduli space of polynomials: we show the equidistribution of Misiurewicz 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 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.
Cite
@article{arxiv.1602.00925,
title = {Distribution of postcritically finite polynomials iii: Combinatorial continuity},
author = {Thomas Gauthier and Gabriel Vigny},
journal= {arXiv preprint arXiv:1602.00925},
year = {2016}
}