Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

Davoud Cheraghi
Arxiv ID: 0712.3490Last updated: 2/9/2022
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.

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