The geometry of fractal sets: Contents
The geometry of fractal sets: Contents
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DOI：
10.1017/cbo9780511623738
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
K. Falconer
中科院分区：
文献类型：
--
作者：
K. Falconer
这本书包含了一个严格的数学处理的几何方面的集的积分和分数Hausdorff维数。局部密度的问题和存在的切线等集的研究，以及在各个方向上的投影的尺寸特性。在整维集的情况下，规则的“曲线状”集和不规则的“灰尘状”集之间的显着差异被展出。该理论通过对偶性与Kayeka集（包含各个方向的线的零区域集）相关。最后一章包括不同的例子集的一般理论是适用的：曲线的分数维，自相似集，奇怪的吸引子的讨论，并从数论的例子，凸性等。有一个重点的基本工具的主题，如维塔利覆盖引理，净措施和傅立叶变换方法。
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular'curve-like'sets and irregular'dust like'sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.