Combinatorial rigidity for unicritical polynomials
Dynamical Systems
2007-05-23 v1
Abstract
We prove that any unicritical polynomial which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the ``Multibrot set'') is locally connected at the corresponding parameter values. It generalizes Yoccoz's Theorem for quadratics to the higher degree case.
Keywords
Cite
@article{arxiv.math/0507240,
title = {Combinatorial rigidity for unicritical polynomials},
author = {Artur Avila and Jeremy Kahn and Mikhail Lyubich and Weixiao Shen},
journal= {arXiv preprint arXiv:math/0507240},
year = {2007}
}
Comments
LaTeX, 12 pages