BOUNDS FOR DIMENSION OF THE ATTRACTOR OF A SCALED IFS

被引：4

作者：

Minirani, S. ^{[1
]}

Mathew, Sunil ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Calicut 673601, Kerala, India

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2013年 / 6卷 / 02期

关键词：

Hausdorff dimension; iterated function system; self-similar sets; similarity dimension;

D O I：

10.1142/S1793557113500289

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A hyperbolic iterated function system (IFS) consists of a complete metric space X together with a finite set of contraction mappings on X. In this paper, the notion of scaled IFS is defined and its existence conditions are examined. The relation between the similarity dimension of the attractors of a given homogeneous IFS and a scaled IFS and its dependency on the scaling factor are studied. A lower and upper bounds for the Hausdorff dimension of the attractor of a scaled IFS is obtained.

引用

页数：10

共 17 条

[1]

Addison P.S., 1997, FRACTALS CHAOS ILLUS

[2]

Barnsley M.F., 1988, FRACTALS EVERYWHERE, V3rd ed.

[3]

Edgar G., 2008, MEASURE TOPOLOGY FRA

[4]

Falconer K., 1997, TECHNIQUES FRACTAL G

[5]

Falconer K., 1985, GEOMETRY FRACTAL SET, DOI 10.1017/CBO9780511623738

[6]

Falconer K., 2004, FRACTAL GEOMETRY MAT

[7] SUB-SELF-SIMILAR SETS [J].

FALCONER, KJ .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (08) :3121-3129

[8] On the structures of generating iterated function systems of Cantor sets [J].

Feng, De-Jun ;

Wang, Yang .

ADVANCES IN MATHEMATICS, 2009, 222 (06) :1964-1981

[9] FRACTALS AND SELF SIMILARITY [J].

HUTCHINSON, JE .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) :713-747

[10]

Kumar P., 2000, THESIS

← 1 2 →