Measure and dimension for some fractal families
Measure and dimension for some fractal families
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DOI：
10.1017/s0305004198002680
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发表时间：
1998-11
影响因子：
0.8
通讯作者：
B. Solomyak
中科院分区：
文献类型：
--
作者：
B. Solomyak
我们研究在线和平面上具有重叠的自相似集。结果表明，存在非整数豪斯多夫维数等于相似维数但豪斯多夫测度为零的自相似集。在许多情况下，豪斯多夫维数是针对典型参数值计算的。我们还探索了自仿射集豪斯多夫维数的 Falconer 公式的有效性条件，并研究了一些分形图的维数。
We study self-similar sets with overlaps, on the line and in the plane. It is shown that there exist self-similar sets that have non-integral Hausdorff dimension equal to the similarity dimension, but with zero Hausdorff measure. In many cases the Hausdorff dimension is computed for a typical parameter value. We also explore conditions for the validity of Falconer's formula for the Hausdorff dimension of self- affine sets, and study the dimension of some fractal graphs.