Hausdorff dimensions in Engel expansions
Hausdorff dimensions in Engel expansions
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DOI：
10.4064/aa99-1-7
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发表时间：
2001
期刊：
影响因子：
0.7
通讯作者：
Yanyan Liu;Jun Wu
中科院分区：
文献类型：
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作者：
Yanyan Liu;Jun Wu
(I)求出(2)失效的集合的Hausdorff维。(Ii)对任意k≥1，设Ak={x∈(0，1]：Log Dn(X)≥kn for any n≥1}.求集合AK的Hausdorff维。对于(I)，第二作者[4]证明了(2)失效的集合的Hausdorff维数为1。本文得到了比(I)和(II)更强的结果。我们证明了定理。对任意α≥1，设A(α)={x∈(0，1]：limn→∞d n(X)=α}.
(i) Find the Hausdorff dimension of the set where (2) fails. (ii) For any k ≥ 1, let Ak = {x ∈ (0, 1] : log dn(x) ≥ kn for any n ≥ 1}. Find the Hausdorff dimension of the set Ak. For (i), the second author [4] has proved that the Hausdorff dimension of the set where (2) fails is 1. In this paper, we get a stronger result than those in (i) and (ii). We show Theorem. For any α ≥ 1, let A(α) = {x ∈ (0, 1] : lim n→∞ d n (x) = α}.