Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

被引：10

作者：

Boore, G. C. ^{[1
]}

Falconer, K. J. ^{[1
]}

机构：

[1] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2013年 / 154卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1017/S0305004112000576

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.

引用

页码：325 / 349

页数：25

共 16 条

[1]

[Anonymous], 1973, Non-negative Matrices and Markov Chains

[2] Exact Hausdorff measure and intervals of maximum density for Cantor sets [J].

Ayer, E ;

Strichartz, RS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (09) :3725-3741

[3]

Barnsley M., 1993, FRACTALS EVERYWHERE

[4]

BOORE G. C., 2011, THESIS ST ANDREWS U

[5] Every set of finite Hausdorff measure is a countable union of sets whose Hausdorff measure and content coincide [J].

Delaware, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (08) :2537-2542

[6]

EDGAR GA, 1992, P LOND MATH SOC, V65, P604

[7]

Edgar GA, 2000, MEASURE TOPOLOGY FRA

[8] Self-similar and self-affine sets: measure of the intersection of two copies [J].

Elekes, Marton ;

Keleti, Tamas ;

Mathe, Andras .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2010, 30 :399-440

[9]

Falconer K., 1997, Techniques in Fractal Geometry

[10]

Falconer K., 2003, FRACTAL GEOMETRY MAT, DOI DOI 10.1002/0470013850

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