Some dimensional results for homogeneous Moran sets
Some dimensional results for homogeneous Moran sets
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DOI：
10.1007/bf02896955
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发表时间：
1997-05
期刊：
影响因子：
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通讯作者：
De-Jun Feng;Z. Wen;Jun Wu
中科院分区：
文献类型：
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作者：
De-Jun Feng;Z. Wen;Jun Wu
设<$（<$nk <$k <$1，<$ck <$k <$1）是由<$nk <$k <$1和<$ck <$k <$1确定的齐次Moran集的集合，其中<$nk <$k <$1是正整数序列，<$ck <$k <$1是正数序列.然后确定了图中元素的Hausdorff维数的最大值和最小值。证明了对于最大值和最小值之间的任意值，存在一个元素使得它的Hausdorff维数等于.同样的结果也适用于包装尺寸。同时，还讨论了齐次Moran集的其它一些性质.
Let ℳ(¦nk¦k⩾1,¦ck¦k⩾1) be the collection of homogeneous Moran sets determined by ¦nk¦k⩾1 and ¦ck¦k⩾1, where ¦nk¦k⩾1 is a sequence of positive integers and ¦ck¦k⩾1 a sequence of positive numbers. Then the maximal and minimal values of Hausdorff dimensions for elements in ℳ are determined. The result is proved that for any valuesbetween the maximal and minimal values, there exists an element in ℳ(¦nk¦k⩾1,¦ck¦k⩾1) such that its Hausdorff dimension is equal tos. The same results hold for packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.