Local connectivity of Julia sets for unicritical polynomials

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dc.creatorKahn, Jeremy
dc.creatorLyubich, Mikhail
dc.date2005-05-10
dc.date.accessioned2026-07-07T05:19:47Z
dc.date.available2026-07-07T05:19:47Z
dc.descriptionWe prove that the Julia set $J(f)$ of at most finitely renormalizable unicritical polynomial $f:z\mapsto z^d+c$ with all periodic points repelling is locally connected. (For $d=2$ it was proved by Yoccoz around 1990.) It follows from a priori bounds in a modified Principle Nest of puzzle pieces. The proof of a priori bounds makes use of new analytic tools developed in math.DS/0505191 that give control of moduli of annuli under maps of high degree.
dc.descriptionLaTeX, 14 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0505194
dc.identifierhttp://arxiv.org/abs/math/0505194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75144
dc.subjectDynamical Systems
dc.subject37F45
dc.titleLocal connectivity of Julia sets for unicritical polynomials
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