关于自相似集的上凸密度研究的最新进展

Some Latest Advances in Upper Convex Density

介绍关于自相似集的上凸密度研究的若干最新进展.利用上凸密度的定义和自相似集的自相似结构,得到自相似集的上凸密度的刻画,进而得到自相似集的上凸密度下限估计的一般方法,并将此方法应用于经典的自相似集.

In this paper, we show some latest advances in upper convex density for the self-similar sets. Using the definition of upper convex density and the self-similar constructure of the self-similar sets, we obtain the characteristic of upper convex density of the self-similar sets. Moreover, we get the general method for estumating the lower bounds of the upper convex density of self-similar sets. At last, we apply the method to some classical fractals.