不动点理论在分形几何中的应用

Application of Theorems of Fixed Point to Fractal Geometry

文章探讨了不动点理论在分形几何中的重要应用.Banach压缩映射不动点定理保证了自相似集这个不动点的存在惟一性及迭代收敛性,促进了分形几何中重要的理论分支——自相似集的产生,另外,相似压缩不动点的有关理论部分回答了关于自相似集的公开问题,为自相似集的研究提供了新的研究方向和思想方法.

The important applications of theorems of the fixed point to fractal geometry were explored in thin article.Firstly,the existence,uniqueness and monotone iterative techniques f self-similar sets is proved by the theory of Banach fixed point theorem,which promote the production of the branch of fractal geometry self-similar set.Secondly,the theorems about the contracting-similarity fixed point for the self-similar sets answers the open problems,which provide a new method for the study of self-similar sets.