Abstract
Let ℳ(¦n k ¦k⩾1,¦c k ¦k⩾1) be the collection of homogeneous Moran sets determined by ¦n k ¦k⩾1 and ¦c k ¦k⩾1, where ¦n k ¦k⩾1 is a sequence of positive integers and ¦c k ¦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 values between the maximal and minimal values, there exists an element in ℳ(¦n k ¦k⩾1,¦c k¦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.
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Project supported by the National Climbing Project “Nonlinear Science” and the Scientific Foundation of the State Education Commission of China.
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Feng, D., Wen, Z. & Wu, J. Some dimensional results for homogeneous Moran sets. Sci. China Ser. A-Math. 40, 475–482 (1997). https://doi.org/10.1007/BF02896955
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DOI: https://doi.org/10.1007/BF02896955