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ZHANG Yun-xiu. Dimension of the intersection of the Cantor ternary set with its two translations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 91-95.
Citation:
ZHANG Yun-xiu. Dimension of the intersection of the Cantor ternary set with its two translations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 91-95.
ZHANG Yun-xiu. Dimension of the intersection of the Cantor ternary set with its two translations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 91-95.
Citation:
ZHANG Yun-xiu. Dimension of the intersection of the Cantor ternary set with its two translations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 91-95.
Let C be the Cantor ternary set. The condition of the intersection C\cap (C+t)\cap (C+s)\neq\emptyset was considered and the Hausdorff dimension of (t,s) was computed when the intersection was nonempty. A conclusion was proved: dim_H C\cap (C+t)\cap (C+s)=0 for a.e. (t,s)\in{\bf R}\times {\bf R}. Then by a related result of Moran set, the expression of dim_H C\cap (C+t)\cap (C+s) was investigated.
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