三分康托集与其两个平移交的维数(英文)

Dimension of the intersection of the Cantor ternary set with its two translations

C为三分康托集,考虑何时交集C∩(C+t)∩(C+s)非空,计算出当交集非空时(t,s)的Hausdorff维数.证明了:对于平面上几乎处处的(t,s),dim_HC∩(C+t)∩(C+s)=0.利用Moran集的相关结论得到当交集非空时dim_H C∩(C+t)∩(C+s)的表达式.

Let C be the Cantor ternary set. The condition of the intersection C （C ＋t） （C ＋ s） ≠ 0 was considered and the Hausdorff dimension of （t, 8） was computed when the intersection was nonempty. A conclusion was proved： dimH C （C ＋ t） n （C ＋ s） ： 0 for a.e. （t, s） ∈ R × R. Then by a related result of Moran set, the expression of dimH C （C ＋ t） n （C ＋ s） was investigated.