一类一维齐次Moran集的维数结果

Results of the dimensions of a class of one dimensional homogeneous Moran sets

为了研究一维齐次Moran集的维数,利用由基本区间形成的连通分支构造了一类{m_(k)}-齐次Moran集,证明该类集合的packing维数和上盒维数在supk{m_(k)}<∞时为所有一维齐次Moran集对应维数的最小值。此外,对于该类集合的上盒维数,得到在一些条件下的取值范围,并找到其达到准确值的一个充分条件。

In order to study the dimensions of one dimensional homogeneous Moran set,a class of homogeneous Moran set,{m_(k)}-homogeneous Moran set,is constructed by the connected components of the basic intervals,and the packing dimensions and the upper box dimensions of the sets are shown to obtain the minimum value of the one dimensional homogeneous Moran set under the condition sup k{m_(k)}<∞.Furthermore,the range of the upper box dimensions of the sets is obtained under some conditions,and a sufficient condition under which the upper box dimension gets the accurate value is found.