Distribution of postcritically finite polynomials
Dynamical Systems
2013-02-05 v1 Complex Variables
Number Theory
Abstract
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.
Cite
@article{arxiv.1302.0810,
title = {Distribution of postcritically finite polynomials},
author = {Charles Favre and Thomas Gauthier},
journal= {arXiv preprint arXiv:1302.0810},
year = {2013}
}