本项目致力于研究回复性与相关动力学性质之间的深刻联系，将主要考虑拓扑动力系统领域与回复性相关的三个方面的研究热点，以期解决有关的若干基本问题，加深人们对动力系统回复性的理解，丰富动力系统的回复性理论。具体说来：..1) 我们将研究某些特定回复族的敏感性，获得与Auslander-Yorke二分法则类似的结果，进一步，将研究敏感性对族回复性的依赖性，以揭示族回复性与敏感性之间的联系；..2) 我们将研究给定Furstenberg族F的F-omega极限集，以及由之产生的包括传递紧致性在内的各种动力学紧致性，进一步，探讨它们与回复性、敏感性等之间的联系；..3) 我们通过研究可数群作用的熵等复杂性函数与点对的渐近性、子集的局部复杂性等之间的关系，以揭示可数群作用的回复性与熵等复杂性函数之间的联系。

In this project, we mainly consider the relationship between recurrence and related dynamical properties, and shall study it from three aspects. Precisely,..1) We shall study sensitivity for some special Furstenberg families, obtain for them analog results of the Auslander-Yorke dichotomy theorem concerning sensitivity, moreover, we shall study the dependence of sensitivity on different Furstenberg families;..2) We shall study the structure of F-omega limit set for a given Furstenberg family F, we shall also study various dynamical compactness (including transitive compactness) induced by these new omega limit sets, furthermore, we shall consider the relationship between these dynamical compactness and recurrence, sensitivity in topological dynamics;..3) Given a topological dynamical system of a countable group action, we shall study the relationship between its complexity function (including entropy function) and recurrence by considering asymptotic behavior of a pair of points and local complexity of a subset in such a system with positive entropy...We wish we could solve some basic problems related to recurrence in topological dynamics with this project, and then understand very well the recurrence behavior in dynamical system and related topics.