论文标题
抛物线盆内的动态
Dynamics inside Parabolic Basins
论文作者
论文摘要
在本文中，我们研究了抛物线盆内轨道的行为。令$ f（z）= z+az^{m+1}+（\ text {imper Term}），m \ geq1，a \ neq0。$我们选择一个任意常数$ c> 0 $和apoint $ q \ in {\ bf v_j}然后存在一个$ z_0 \ in \ mathcal {p} _j $，以便对于任何$ \ tilde {q} \ in q：= \ cup_ {l = 0}^{\ infty} {\ infty} f^{ - l}（ - l}（f^k（q）（f^k（q）） {p} _j}（z_0，\ tilde {q}）> c $，其中$ d _ {\ mathcal {p} _j} $是kobayashi metric。在上一篇论文[4]中，我们表明该结果对于吸引盆地无效。
In this paper, we investigate the behavior of orbits inside parabolic basins. Let $f(z)=z+az^{m+1}+(\text{higher terms}), m\geq1, a\neq0.$ We choose an arbitrary constant $C>0$ and a point $q\in{\bf v_j}\cap\mathcal{P}_j$. Then there exists a point $z_0\in \mathcal{P}_j$ so that for any $\tilde{q}\in Q:= \cup_{l=0}^{\infty}f^{-l}(f^k(q)) (l, k$ are non-negative integers), the Kobayashi distance $d_{\mathcal {P}_j}(z_0, \tilde{q})> C$, where $d_{\mathcal{P}_j}$ is the Kobayashi metric. In a previous paper [4], we showed that this result is not valid for attracting basins.
