本项目主要研究拓扑动力系统中的混沌和维数理论这两个方面。一方面，我们研究由连续映射诱导的动力系统的混沌行为。弱混合系统的复杂性备受大家的关注，我们将研究整个空间能否作为弱混合系统的混沌集这个问题和弱混合系统具有迭代不变一致分离的混沌集的条件。我们还将研究平均意思下的混沌，敏感性和等度连续属性，以及它们与其它动力学性质之间的关系。另一方面，我们研究amenable群作用下动力系统的维数理论，侧重于研究拓扑熵，测度熵，空间Hausdorff维数和混沌集的Hausdorff维数之间的关系。

In this project, we study the chaos theory and dimension theory in topological dynamics. On the one hand, we study the chaotic behavior of dynamical systems induced by a continuous self-map. The complexity of weakly mixing systems have aroused great interest, we will study the open problem that whether the whole space of a weakly mixing system can be a chaotic set and under what conditions a weakly mixing system must have uniformly separated invariant chaotic sets. We will also study chaos, sensitivity and equicontinuity properties in the mean sense, and their relationship with other important dynamical properties. On the other hand, we study the dimension theory of dynamical systems under amenable group actions. We will focus on the relations among topological entropy, measure-theoretical entropy, Hausdorff dimension of the space and chaotic sets.