论文标题
多项式朱莉娅集的凸壳
Convex hulls of polynomial Julia sets
论文作者
论文摘要
我们证明了P. Alexandersson的猜想，对于每一个复杂的多项式$ p $ a $ d \ geq 2 $ convex hull $ h_p $ of julia set set $ j_p $ of $ p $ $ p $ a $ p $ p $ p^{ - 1}（h_p）（h_p）\ subset h_p $。我们进一步证明，仅当$ p $与chebyshev polyenmial $ t_d $ d $ d $，至$ -t_d $或单元$ c z^d $ a $ c z = 1 $ | = 1 $时，我们只有在与chebyshev polyenmial $ t $ $ d $ of p $ a $ p $相关时，才能实现平等$ p^{ - 1}（h_p）= h_p $。
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 only if $p$ is affinely conjugated to the Chebyshev polynomial $T_d$ of degree $d$, to $-T_d$ or a monomial $c z^d$ with $|c|=1$.
