正则分歧有理函数的动力系统及相关问题的研究

正则分歧有理函数是一类重要的复解析函数，Milnor最先研究了一类特殊的正则分歧有理函数的动力系统。本项目计划研究更一般的正则分歧有理函数的动力系统。主要包含下面四个方面的内容：1、正则分歧有理函数Julia集的局部连通性，拓扑分类。2、只有三个临界值的有理函数的Herman环的存在性。3、Julia集为exploded McMullen necklace的有理函数。4、广义McMullen函数的Julia集的Hausdorff维数。

Regularly ramified rational functions are a kind of important complex analytic functions. Milnor studied the dynamical system of a special kind of regularly ramified rational functions. This project plans to study the dynamical system of more general regularly ramified rational functions. It mainly includes the following four aspects: 1、The local connectivity and the topological classification of Julia sets of regularly ramified rational functions. 2、The existence of Herman rings of rational functions with only three critical values. 3、Rational functions whose Julia sets are exploded McMullen necklaces. 4、The Huasdorff dimensions of Julia sets of the generalized McMullen functions.