Assouad type dimensions and homogeneity of fractals
Assouad type dimensions and homogeneity of fractals
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DOI：
10.1090/s0002-9947-2014-06202-8
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发表时间：
2013-01
影响因子：
1.3
通讯作者：
J. Fraser
中科院分区：
文献类型：
--
作者：
J. Fraser
我们调查了几个方面的Assouad维度和较低的维度，它们一起形成一个自然的“维度对”。特别是，我们计算这些尺寸为某些类的自仿射集和拟自相似集，并研究它们与其他概念的尺寸，如Hausdorff尺寸的关系。我们还调查了这些方面的一些基本性质，包括他们的行为工会和产品和他们的集合论的复杂性。
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural ‘dimension pair’. In particular, we compute these dimensions for certain classes of self-affine sets and quasiself-similar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.