论文标题
逃脱的Meromororphic函数集的Hausdorff尺寸
Hausdorff dimension of escaping sets of meromorphic functions
论文作者
论文摘要
我们完整地描述了具有有限数量的单数值的Meromormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormor的描述。更确切地说，对于[0,2] $中的任何给定的$ d \，我们表明存在这样的Meromororphic函数，其逃逸集的Hausdorff尺寸等于$ d $。主要成分是通过使用准文献映射将合适的Meromormormormormormormormormormormormormormormormormormormorthic函数粘合在一起。此外，我们表明，逃逸集的eScaper sets具有不同的hausdorff尺寸，存在许多无数形式等效的异形函数。
We give a complete description of the possible Hausdorff dimensions of escaping sets for meromorphic functions with a finite number of singular values. More precisely, for any given $d\in [0,2]$ we show that there exists such a meromorphic function for which the Hausdorff dimension of the escaping set is equal to $d$. The main ingredient is to glue together suitable meromorphic functions by using quasiconformal mappings. Moreover, we show that there are uncountably many quasiconformally equivalent meromorphic functions for which the escaping sets have different Hausdorff dimensions.
