论文标题
周期性点和光滑的光线
Periodic Points and Smooth Rays
论文作者
论文摘要
令$ p：{\ mathbb c} \ to {\ mathbb c} $是一张多项式地图，带有断开连接的填充julia set $ k_p $，让$ z_0 $是$ p $的排斥或抛物线的定期点。我们表明，如果包含$ z_0 $的$ k_p $的连接组件是非排级的，则$ z_0 $是至少一个{\ it平滑}外部射线的着陆点。从某种意义上说，该声明是最佳的，因为除了一射线以$ z_0 $降落以外的所有射线都可能被打破。
Let $P: {\mathbb C} \to {\mathbb C}$ be a polynomial map with disconnected filled Julia set $K_P$ and let $z_0$ be a repelling or parabolic periodic point of $P$. We show that if the connected component of $K_P$ containing $z_0$ is non-degenerate, then $z_0$ is the landing point of at least one {\it smooth} external ray. The statement is optimal in the sense that all but one ray landing at $z_0$ may be broken.
