Diophantine逼近是数论研究中的一个热门分支，而关于精确Diophantine理论的研究涉及了分形几何、数的表示理论以及Lagrange谱的研究，无论在理论基础上还是实际应用中都有极其重要的意义。该项目主要就精确Diophantine逼近的度量性质与分形结构展开研究，主要探讨以下几类问题：1、可以被精确逼近的点所组成的集合的度量理论与分形理论；2、在三分Cantor集上可以被精确逼近的点组成的度量性质与分形结构；3、形式级数域上的精确Diophantine逼近的度量理论和分形理论。上述问题的解决将有助于推动分形几何与Diophantine逼近领域间的交叉发展。

Diophantine approximation is a hot branch in the study of number theory, and the research of exact Diophantine theory involves fractal geometry, representation theory of number and the research of Lagrange spectrum. It has very important significance both in theoretical basis and practical application. This project conducts a study mainly about metric properties and fractal structures of exact Diophantine approximation. It chiefly discusses a few problems as follows:1, the measure theory and the fractal theory of the points of exact approximation. 2, the metric properties and fractal structures of the points of exact approximation in the trisection cantor sets. 3, the measure theory and fractal theory of exact Diophantine approximation in the formal power series field. The solution of the problems above will help promote the interactive development of the fields between the fractal geometry and Diophantine approximation ..　　　.