HAUSDORFF AND BOX DIMENSIONS OF CERTAIN SELF AFFINE FRACTALS

被引：110
作者：
LALLEY, SP
GATZOURAS, D
机构：
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 1992年 / 41卷 / 02期
关键词：
D O I：
10.1512/iumj.1992.41.41031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Hausdorff Besicovich and Bouligand Mirikowski (box) dimensions delta(H) and delta(B) are computed for a class of self-affine sets. Necessary and sufficient conditions are given for delta(H) = delta(B); it is found that typically delta(H) not-equal delta(B). The methods are largely probabilistic, with certain exponential families of probability measures playing a prominent role.
引用
收藏
页码：533 / 568
页数：36
相关论文
共 12 条
[1]  
[Anonymous], 1991, INTRO PROBABILITY TH
[2]   ON WEIERSTRASS-LIKE FUNCTIONS AND RANDOM RECURRENT SETS [J].
BEDFORD, T .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1989, 106 :325-342
[3]   THE BOX AND HAUSDORFF DIMENSION OF SELF-AFFINE SETS [J].
BEDFORD, T ;
URBANSKI, M .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1990, 10 :627-644
[4]  
BILLINGLSEY P, 1986, PROBABILITY MEASURE
[5]   THE HAUSDORFF DIMENSION OF SELF-AFFINE FRACTALS [J].
FALCONER, KJ .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 103 :339-350
[6]   FRACTALS AND SELF SIMILARITY [J].
HUTCHINSON, JE .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) :713-747
[7]  
Mandelbrot B.B., 1983, AMJPHYS
[8]   THE HAUSDORFF DIMENSION OF GENERAL SIERPINSKI CARPETS [J].
MCMULLEN, C .
NAGOYA MATHEMATICAL JOURNAL, 1984, 96 (DEC) :1-9
[9]   SELF-SIMILAR MEASURES AND THEIR FOURIER-TRANSFORMS .1. [J].
STRICHARTZ, RS .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1990, 39 (03) :797-817
[10]  
WELLER W, 1986, INTRO PROBABILITY IT, V1
12