Dimensions of a class of high-dimensional homogeneous Moran sets and Moran classes

作者：Yan P^*

来源：Progress in Natural Science, 2002, 12(9): 655-660.

• Moran set
• Moran class
• homogeneous Cantor set
• partial homogeneous Cantor set
• dimension

A class of high-dimensional homogeneous Moran sets and Moran classes are introduced and some dimensional properties are studied. The Hausdorff dimension, modified lower box-counting dimension, lower and upper box-counting dimension, and packing dimension of high-dimensional homogeneous and partial homogeneous Cantor sets are determined. Moreover, a kind of fractal E is obtained, which is not regular but with the property Dim(w)(E-d) - dDim(w)(E), where w denotes any of the dimensions mentioned above.

• 出版日期2002-9
• 单位清华大学