Combinatorial rigidity for unicritical polynomials

Details Combinatorial rigidity for unicritical polynomials Combinatorial rigidity for unicritical polynomials

2005-07-12

arxiv.org/abs/math/0507240v1

Mathematics

Dynamical Systems

LaTeX, 12 pages

Scientific paper

We prove that any unicritical polynomial $f_c:z\mapsto z^d+c$ 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.

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