Measures and dimensions of fractal sets in local fields

被引：0
|
作者：
QIU Hua** and SU Weiyi(Department of Mathematics
机构：
来源：
Progress in Natural Science:Materials International | 2006年 / 12期
基金：
中国国家自然科学基金;
关键词：
local field; p-series field; Hausdorff measure and dimension; Boxcounting dimension; Packing measure and dimension; Cantor type set;
D O I：
暂无
中图分类号：
O177 [泛函分析];
学科分类号：
070104 ;
摘要：
The study of fractal analysis over the local fields as underline spaces is very important since it can motivate new approaches and new ideas, and discover new techniques in the study of fractals. To study fractal sets in a local field K, in this paper, we define several kinds of fractal measures and dimensions of subsets in K. Some typical fractal sets in K are constructed. We also give out the Hausdorff dimensions and measures, Box-counting dimensions and Packing dimensions, and stress that there exist differences between fractal analysis on local fields and Euclidean spaces. Consequently, the theoretical foundation of fractal analysis on local fields is established.
引用
收藏
页码：1260 / 1268
页数：9
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