Distribution of points with prescribed derivative in polynomial dynamics
Dynamical Systems
2016-06-20 v1 Complex Variables
Abstract
In analogy to the equidistribution of preimages of a prescribed point by the iterates of a polynomial map in the complex plane towards the equilibrium measure, we show here the equidistribution of points for which the derivative of the n-th iterate of the polynomial takes a suitable prescribed value towards the equilibrium measure. We then give a similar statement in the space of degree d polynomials for the equidistribution of parameters for which the n-derivative at a given critical value has a prescribed derivative towards the activity current of the corresponding critical point.
Keywords
Cite
@article{arxiv.1606.05422,
title = {Distribution of points with prescribed derivative in polynomial dynamics},
author = {Thomas Gauthier and Gabriel Vigny},
journal= {arXiv preprint arXiv:1606.05422},
year = {2016}
}