HAUSDORFF DIMENSION OF CERTAIN RANDOM SELF-AFFINE FRACTALS

被引：3
|
作者：
Luzia, Nuno [1 ]
机构：
[1] Univ Fed Rio de Janeiro, Rio de Janeiro, Brazil
来源：
STOCHASTICS AND DYNAMICS | 2011年 / 11卷 / 04期
关键词：
Hausdorff dimension; random; variational principle; FULL DIMENSION;
D O I：
10.1142/S0219493711003516
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this work we are interested in the self-affine fractals studied by Gatzouras and Lalley [5] and by the author [11] who generalize the famous general Sierpinski carpets studied by Bedford [1] and McMullen [13]. We give a formula for the Hausdorff dimension of sets which are randomly generated using a finite number of self-affine transformations each generating a fractal set as mentioned before. The choice of the transformation is random according to a Bernoulli measure. The formula is given in terms of the variational principle for the dimension.
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页码：627 / 642
页数：16
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