Combinatorial rigidity for unicritical polynomials

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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.
LaTeX, 12 pages

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Dynamical Systems, 37F45

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http://salesiana.dossiersoluciones.com/handle/123456789/75755

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0507240
 http://arxiv.org/abs/math/0507240

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arXiv