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arXiv:0712.3490 [math.DS]AbstractReferencesReviewsResources

Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

Davoud Cheraghi

Published 2007-12-20, updated 2010-03-02Version 3

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.

Comments: 47 Pages; 7 figures; changes in some proofs; Changes in the writing
Categories: math.DS
Subjects: 37F45, 37F25, 37F30
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