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|Title:||Combinatorial rigidity for unicritical polynomials|
|Citation:||Avila, A., Kahn, J., Lyubich, M., Shen, W. (2009). Combinatorial rigidity for unicritical polynomials. Annals of Mathematics 170 (2) : 783-797. ScholarBank@NUS Repository. https://doi.org/10.4007/annals.2009.170.783|
|Abstract:||We prove that any unicritical polynomial fc : z → zd + 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.|
|Source Title:||Annals of Mathematics|
|Appears in Collections:||Staff Publications|
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