有理函数动力系统中的一个基本问题是：如何理解和刻画有理函数动力系统的组合结构。而研究这个问题的关键在于构造动力系统的组合不变量。在本项目中，我们计划对Newton映射和临界有限有理函动力系统构造一种组合不变量--不变图，并利用它来研究相关的动力系统问题。具体的研究内容如下：.1、研究次数大于3的Newton映射的动力系统，包括Julia集的局部连通性，重整化和游荡连续统问题。.2、给出临界有限有理函数动力系统的一种分解方法，为研究有理函数动力系统提供一条新的思路。.3、对临界有限有理函数动力系统构造一种组合不变量：不变图，从而为研究有理函数动力系统提供工具。.4、应用上面提到的分解方法和不变图研究临界有限有理函数的游荡连续统问题。

A fundamental question in the dynamics of rational maps is that: how to understand and characterize the combinatorial structure of the dynamics of rational maps. The key point to study this problem is to construct a combinatorial invariant for the dynamics. In this project, we plan to construct a combinatorial invariant--invariant graphs for Newton maps and postcritically finite rational maps, and then study the corresponding dynamics by the invariant graphs. The project includs the following items:.1. We will study the dynamics of Newton map of degree more than 3, including the local connectivity of the Julia set, the renomorlization and wandering continuum problems..2. We will give a decomposition method for the dynamics of postcritically finite rational maps, which provides a new idea to study the dynamics of rational maps..3. We will construct a combinatorial invariant for postcritically finite rational maps, called invariant graph, which is a powerful tool to study the dynamics of rational maps..4. Applying the decomposition method and invariant graph mentioned above, we will study the wandering continuum for postcritically finte rational maps.