Institute for Mathematical Sciences
Artur Avila, Jeremy Kahn, Mikhail Lyubich and Weixiao Shen
Combinatorial rigidity for unicritical polynomials
Abstract: 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
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