Combinatorial rigidity for some infinitely renormalizable unicritical polynomials
Dynamical Systems
2022-02-09 v4
Abstract
We prove combinatorial rigidity of infinitely renormalizable unicritical polynomials, P_c :z \mapsto z^d+c, with complex c, under the a priori bounds and a certain "combinatorial condition". This implies the local connectivity of the connectedness loci (the Mandelbrot set when d = 2) at the corresponding parameters.
Cite
@article{arxiv.0712.3490,
title = {Combinatorial rigidity for some infinitely renormalizable unicritical polynomials},
author = {Davoud Cheraghi},
journal= {arXiv preprint arXiv:0712.3490},
year = {2022}
}
Comments
37 Pages; 7 figures; pre-publication version