Graph-directed iterated function systems with overlaps

被引：22

作者：

Das, M ^{[1
]}

Ngai, SM

机构：

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Georgia So Univ, Dept Math Sci, Statesboro, GA 30460 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2004年 / 53卷 / 01期

关键词：

graph-directed iterated function system; graph self-similar set; finite type condition; box dimension; Hausdorff dimension; Hausdorff measure;

D O I：

10.1512/iumj.2004.53.2342

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we describe algorithms to compute the box dimension and Hausdorff dimension of the corresponding graph self-similar sets and show that these dimensions agree; moreover, the Hausdorff measure of these sets is shown to be strictly positive.

引用

页码：109 / 134

页数：26

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