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Combinatorial rigidity for unicritical polynomials
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DOI：10.4007/annals.2009.170.783.png)
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Abstract
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We prove that any unicritical polynomial f(c) : z bar right arrow z(d) + c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. This implies that the connectedness locus (the Multibrot set) is locally connected at the corresponding parameter values and generalizes Yoccoz's Theorem for quadratics to the higher degree case.
Keywords:
LOCAL CONNECTIVITY
MANDELBROT
DYNAMICS
FAMILIES
SETS
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5.3
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1.4K
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