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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
MathSciNet review: 4172601
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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 $|c|=1$.


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Małgorzata Stawiska
Affiliation: Mathematical Reviews, 416 Fourth Street, Ann Arbor, Michigan 48103
ORCID: 0000-0001-5704-7270
Email: stawiska@umich.edu

Received by editor(s): April 29, 2020
Published electronically: October 9, 2020
Communicated by: Filippo Bracci
Article copyright: © Copyright 2020 American Mathematical Society