Abstract

We prove that any unicritical polynomial f_c : z↦z^d + c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. This implies that the connectedness locus (the “Multibrot set”) is locally connected at the corresponding parameter values and generalizes Yoccoz’s Theorem for quadratics to the higher degree case.

Mathematical Subject Classification

Primary: 37F45

Milestones

Received: 1 August 2005

Authors