论文标题
FATOU集的内部动力学
Interior Dynamics of Fatou Sets
论文作者
论文摘要
在本文中，我们研究了吸引盆地内部轨道的精确行为。令$ f $为$ \ mathbb {c} $，$ \ mathcal {a}（p）$是吸引固定点$ p $ $ f $ $ f $的吸引人的盆地的$ m \ geq2 $的全体形态多项式。我们证明存在一个常数$ c $，因此对于任何$ω_i$内部的每个点$ z_0 $，都存在$ q \ in \ cup_k f^{ - k} $ in $ q \ in \ cup_k f^{ - k}（p）$ insun $ω_i$内部，因此$ d_ {ω_i} $ d_i} $ω_i。$
In this paper, we investigate the precise behavior of orbits inside attracting basins. Let $f$ be a holomorphic polynomial of degree $m\geq2$ in $\mathbb{C}$, $\mathcal {A}(p)$ be the basin of attraction of an attracting fixed point $p$ of $f$, and $Ω_i (i=1, 2, \cdots)$ be the connected components of $\mathcal{A}(p)$. We prove that there is a constant $C$ so that for every point $z_0$ inside any $Ω_i$, there exists a point $q\in \cup_k f^{-k}(p)$ inside $Ω_i$ such that $d_{Ω_i}(z_0, q)\leq C$, where $d_{Ω_i}$ is the Kobayashi distance on $Ω_i.$
