自Furstenberg提出分形集的齐性概念以来，可以从micro-set出发统一分形的诸多局部性质的研究。本项目计划引入广义Furstenberg齐性，通过Ahlfors正则性、密度定理等测度技术研究(强)有限型、弱分离、Furstenberg齐性之间的内在本质联系；对Assouad维数，本项目计划通过拟Assouad维数、一致不连通性等研究在拟Lipschitz映射下Assouad维数的变化。本项目的开展，将有助于从几何结构上进一步加深对自相似集的局部结构的理解。

Furstenberg introduced the homogeneity of fractal in terms of micro-sets. The notion of micro-set gives a new perspective of the study on the local properties of fractals. Introducing the generalized Furstenberg's homogeneity and applying Ahlfors regularity and density approach, we try to study the intrinsic relations among (strong) finite-type, weak sepearation condition and Furstenberg homogeneity. We also plan to invesitage the change of Assouad dimension under quasi-Lipschitz mappings, using quasi-Assouad dimension and uniform disconnectness. The project will help us to further comprehend the local properties of self-similar sets from geometric structure.