一推广Cantor集在相似压缩不动点处的上凸密度

The Upper Convex Density of a Generalized Cantor Set at the Contracting-similarity Fixed Point

在分形几何的研究中,上凸密度提供了的研究自相似分形结构理论和工具.文章利用自相似集在相似压缩不动点处的上凸密度的两个等价定义,探讨一推广Cantor集在其相似压缩不动点处的上凸密度,所得结果对一个相关重要猜测给予了有力支持.

In the study of fractal geometryt,he upper convex density offers the theory and the implement to study the structure of the self-similar fractals for us.In this papert,he upper convex density at a contracting-similarity fixed point of the generalized Cantor set has been studied by using two equivalent definitions.As a resultt,he main result obtained in this papers,upport an important conjecture.