在遍历理论和拓扑动力系统的研究中，许多重要的问题在正熵的条件下取得了突破，但是对于零熵系统却没有本质进展。本项目主要研究目标是零熵动力系统，希望能通过动力系统模型理论、局部化、序列化等思想方法对零熵动力系统的精细结构和复杂性产生机制进行深入研究，并将其应用到 Sarnak 猜测、逐点收敛多重遍历平均问题等重要问题的研究中。具体的研究内容包括：对测度零熵系统得到更为精细的拓扑模型，使得对一些涉及零熵的问题可以同时运用测度与拓扑的方法进行研究；对一些更一般的distal 系统和一些具有较好结构的零熵系统证明 Sarnak 猜测；研究零熵系统的逐点收敛遍历平均问题等。

In ergodic theory and topological dynamics, lots of important open problems were solved for the systems with positive entropy, but remain open for the systems with zero entropy. The main theme of this project is to study systems with zero entropy and related problems. We try to study the systems with zero entropy via topological model, localization etc., and focus on Sarnak conjecture and the problem on pointwise multiple ergodic averages. To be precise, the following problems will be studied: find a more suitable topological model for an ergodic system with zero entropy; prove that Sarnak Conjecture holds for some distal systems and some systems with zero entropy and nice structure; study the problem on pointwise multiple ergodic averages for systems with zero entropy.