刻画有理函数的Julia集的连通性、局部连通性、Hausdorff维数、Hausdorff测度等拓扑特征和分析特征是复动力系统领域中一个重要的问题。本项目将研究单参数正则分歧有理函数的Julia集的局部连通性，只有三个临界值的有理函数的Herman环的存在性问题，Julia集为exploded McMullen necklaces的有理函数等问题。

It is an important problem in complex dynamical systems to characterize the topological properties and analysis properties of the Julia sets of rational functions,such as connectivity, local connectivity, Hausdorff dimension and Hausdorff measure etc.. This project will study the locally connectivity of The Julia sets of regularly ramified rational functions with one parameter, the existence of the Herman ring of rational functions with only three critical values, the existence of the rational functions whose Julia sets are exploded McMullen necklaces etc..