一类d-维齐次Moran集的分形维数

Fractal dimensions of a class of d-dimensional homogeneous Moran Sets

该文研究了一类特殊的d-维齐次Moran集:{m_(k)^(d)}型齐次Moran集,利用质量分布原理、乘积集的分形维数不等式以及关于一维齐次Moran集上盒维数的重要引理,结合{m_(k)^(d)}型齐次Moran集的自身结构,得到了{m_(k)^(d)}型齐次Moran集在特定条件下的Hausdorff维数与上盒维数的表达式.

{m_(k)^(d)}type homogeneous Moran sets,which are a special class of d-dimensional homogeneous Moran sets are studied in this paper.By using the mass distribution principle,the inequality of the fractal dimensions for the product set and the important lemma of the upper box dimension for the one dimensional homogeneous Moran sets are obtained.Meanwhile,combining the structures of{m_(k)^(d)}type homogeneous Moran sets,the representations of Hausdorff dimension and upper box dimension for{m_(k)^(d)}type homogeneous Moran sets are obtained under some conditions.