在遍历理论和拓扑动力系统的研究中，特征因子的思想起了越来越重要的作用。本项目主要对目前动力系统研究中一些热门问题的特征因子进行深入研究，以期得到相应问题的进展。研究内容主要涉及多重作用下动力系统研究、幂零结构理论与熵理论等动力系统研究中的核心课题。具体研究的问题包括：多重作用下动力系统的回复性问题以及多重遍历平均问题的特征因子研究，尤其希望在Furstenberg多重极小点存在问题上取得进展；给出幂零因子产生机制的更多刻画，证明它为所期待解决问题的特征因子，并将之运用到组合数论中的问题研究上；研究涉及熵理论的特征因子问题，例如对Sarnak猜测进行进一步研究，给出有限序列熵系统的拓扑与测度结构等。

In the study of ergodic theory and topological dynamics, the idea of characteristic factors plays an increasingly important role. The main theme of this project is to study the characteristic factors of some important problems in dynamical systems, and try to make some progress. The research content mainly involves the core topics in the dynamical systems such as dynamical properties of systems under multiple actions, nilpotent structure and entropy etc. The specific research questions include: study the characteristic factors of the multiple recurrent problem and the multiple ergodic average problem of dynamical systems under multiple actions, especially hope to make some progress in the Furstenberg's problem on the existence of the multiple minimal points; give more characterizations of the nilfactors, prove that it is the characteristic factor of the problem under study and apply it to some problems in combinatorial number theory; study the characteristic factors of problems involving entropy theory, such as further study of Sarnak conjecture, and give the topological and measurable structure of systems with bounded sequence entropy.