A Random Fractal in the Ring of p-Adic Integers

被引：0

作者：

Kaneko, Hiroshi ^{[1
]}

Nishiwaki, Wakana ^{[1
]}

机构：

[1] Tokyo Univ Sci, Tokyo, Japan

来源：

P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS | 2011年 / 3卷 / 01期

关键词：

Hausdorff dimensions; martingales; p-adic integers; random fractals;

D O I：

10.1134/S2070046611010067

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we will give a construction of a random fractal in the ring of p-adic integers and examine an extent of the random fractals. Paying attention to an importance in statistical self similarity, we will perform measurement for the extent in terms of the Hausdorff dimension similarly to the typical fractal analysis in the Euclidean space. In our study, we will take a measure theoretic approach combined with the martingale theory based on Falconer's method.

引用

页码：74 / 80

页数：7

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