On the Dimension and Measure of Inhomogeneous Attractors
On the Dimension and Measure of Inhomogeneous Attractors
复制标题
非齐次吸引子的维数与测度
DOI：
10.14321/realanalexch.44.1.0199
复制
发表时间：
2018
影响因子：
0.2
通讯作者：
Stuart A. Burrell
中科院分区：
文献类型：
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作者：
Stuart A. Burrell
研究了由迭代函数系统生成的非齐次吸引子的上盒维数。我们的结果可以应用于亲和性维数小于1的仿射系统和满足有界畸变的系统，例如维数大于1的共形系统。特别地，这推广了弗雷泽关于自相似集的结果。我们还应用所开发的方法来研究临界值处的豪斯多夫测度。
We investigate the upper box dimension of inhomogeneous attractors generated from iterated function systems. Our results have applications for affine systems with affinity dimension less than one and systems satisfying bounded distortion, such as conformal systems in dimensions greater than one. In particular, this generalises the result of Fraser on self-similar sets. We also apply the methods developed to investigate the Hausdorff measure at the critical value.