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Convex hulls of polynomial Julia sets
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-09 , DOI: 10.1090/proc/15224
Małgorzata Stawiska

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$.


中文翻译:

多项式Julia集的凸包

摘要:我们证明了P. Alexandersson的猜想,即对于每一个复杂的次数多项式$ p $,Julia集$ d \ geq 2 $的凸包都满足。我们进一步证明了平等实现当且仅当在仿射结合到切比雪夫多项式程度,来,或单项式带。$ H_p $$ J_p $$ p $ $ p ^ {-1}(H_p)\子集H_p $ $ p ^ {-1}(H_p)= H_p $$ p $$ T_d $$ d $$ -T_d $$ cz ^ d $$ \ vert c \ vert = 1 $
更新日期:2020-11-12
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