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Proceedings of the American Mathematical Society

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Convex hulls of polynomial Julia sets


Author: Małgorzata Stawiska
Journal: Proc. Amer. Math. Soc. 149 (2021), 245-250
MSC (2010): Primary 37F10; Secondary 30C15, 52A10
DOI: https://doi.org/10.1090/proc/15224
Published electronically: October 9, 2020
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Abstract: We prove P. Alexandersson's conjecture that for every complex polynomial $ p$ of degree $ d \geq 2$ the convex hull $ H_p$ of the Julia set $ J_p$ of $ p$ satisfies $ p^{-1}(H_p) \subset H_p$. We further prove that the equality $ p^{-1}(H_p) = H_p$ is achieved if and only if $ p$ is affinely conjugated to the Chebyshev polynomial $ T_d$ of degree $ d$, to $ -T_d$, or to a monomial $ c z^d$ with $ \vert c\vert=1$.


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Małgorzata Stawiska
Affiliation: Mathematical Reviews, 416 Fourth Street, Ann Arbor, Michigan 48103
Email: stawiska@umich.edu

DOI: https://doi.org/10.1090/proc/15224
Received by editor(s): April 29, 2020
Published electronically: October 9, 2020
Communicated by: Filippo Bracci
Article copyright: © Copyright 2020 American Mathematical Society