丢番图逼近是数论研究的一个重要分支，近几十年来，随着分形集的出现，开始有了分形集上的丢番图逼近。本项目拟研究最简单的分形集---Cantor集上丢番图逼近的若干性质，具体包括以下三个相关联的问题：（1）研究Cantor集中满足逼近条件限制的点所构成的集合的性态，估计该集合的Hausdorff维数；（2）考察Cantor集中满足精确逼近条件限制的点的存在性；（3）将上述结论推广到形式级数域，解决Beta-展式中丢番图逼近的相关问题。. 本项目是分形几何与丢番图逼近相结合的一个课题，内容涉及丢番图逼近中的热点问题，上述问题的解决将有利于推动双方学科的交叉发展。

Diophantine Approximation is an important branch of Number Theory. Over the last decades, with the emergence of fractals, lots of interests began to focus on Diophantine approximation in fractals. This project intends to study some properties of Diophantine approximation in the simplest fractals ---- Cantor sets, including the following three associated problems: (1) Explore the behavior of the subset of Cantor set constituted by the point satisfying certain approximation conditions, and estimate the Hausdorff dimension of this set; (2) Explore the existence of the point in Cantor set satisfying exact approximation conditions; (3) Extend the conclusions above to the field of formal Laurent series, resolve the associated problems of Beta-expansions.. This project is a combination of Fractal Geometry and Diophantine Approximation, it involves the hot issues in Diophantine Approximation. The solution of the problems above will be conducive to promoting the cross development of both disciplines.