论文标题
逃脱的Meromororphic函数集的Hausdorff维度II
Hausdorff dimension of escaping sets of meromorphic functions II
论文作者
论文摘要
平面中超验和仿产功能的函数至少具有两个奇异值。一方面，如果meromorthic函数完全具有两个单数值，那么众所周知，逃脱集的Hausdorff尺寸只能是$ 2 $或$ 1/2 $。另一方面，Speiser函数的逃逸集的Hausdorff维度可以在$ [0,2] $中获得每个数字（参见\ cite {ac1}）。在本文中，我们表明，达到逃脱集的每个Hausdorff尺寸所需的奇异值数量不超过$ 4 $。
A function which is transcendental and meromorphic in the plane has at least two singular values. On one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either $2$ or $1/2$. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in $[0,2]$ (cf. \cite{ac1}). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than $4$.
