arXiv math/05072402005-07-12math.DS

Combinatorial rigidity for unicritical polynomials

Artur Avila, Jeremy Kahn, Mikhail Lyubich, Weixiao Shen

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英文摘要：

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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