Topological properties of the attractors of iterated function systems

被引：0

作者：

Dumitru, Dan ^{[1
]}

机构：

[1] Spiru Haret Univ Bucharest, Dept Math & Comp Sci, Bucharest, Romania

来源：

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA | 2011年 / 19卷 / 03期

关键词：

attractors; iterated function system; arcwise connected; connected;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate necessary conditions for an attractor of an iterated function system to have a finite number of connected components. Then we prove that each connected component of an attractor of an iterated function system which has a finite number of connected components is also arcwise connected. We also emphasize by a counterexample, that the result does not hold when the attractor has an infinite number of connected components.

引用

页码：117 / 126

页数：10

共 9 条

[1]

Barnsley M., 1993, FRACTALS EVERYWHERE

[2]

Dumitru D., 2008, AN STIINT U BUCUREST, V1, P75

[3]

FALCONER KJ, 1990, FRACTAL GEOMETRY FDN

[4] FRACTALS AND SELF SIMILARITY [J].

HUTCHINSON, JE .

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

[5]

Kigami J., 2001, ANAL FRACTALS

[6]

Miculescu R, 2008, P AM MATH SOC, V136, P587

[7]

Mihail A, 2008, REAL ANAL EXCH, V34, P195

[8]

Secelean A., 2001, Far East J. Dyn. Syst., V3, P149

[9]

YAMAGUTI M, 1997, TRANSLATIONS MATH MO, V167

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