| Hausdorff Dimensions of Some Reduced Homogeneous Moran Sets |
| Received:May 17, 2005 Revised:July 19, 2005 |
| Key Words:
reduced homogeneous Moran set $k$-sequence set Hausdorff dimension.
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| Fund Project:the Natural Science Foundation of Guangxi Province (0339071); the Science Foundation of the Education Department of Guangxi Province ([2003]22) |
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| Abstract: |
| $D_{k}=\{(i_{1},\ldots,i_{k}):1\leq i_{j} \leq n_{j},1 \leq j \leq k \}$ in the iterative process of the homogeneous Moran is reduced to $\tilde{D}_{k}=\{(i_{1},\ldots,i_{k}):1 \leq i_{j} \leq n_{j},i_{j}\neq 2\quad\mbox{unless}\quad i_{j-1}=1,2 \leq j \leq k \}$, the corresponding set is called symmetric cantor set. The Hausdorff dimensions of $\tilde{E}$ are determined. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.02.019 |
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