Exact Hausdorff centered measure of symmetry Cantor sets

Meifeng Dai and Lixin Tian

Chaos, Solitons & Fractals, 2005, vol. 26, issue 2, 313-323

Abstract: Let K(λ1,λ2), the symmetry Cantor sets, be the attractor of an iterated function system {f1,f2,f3} on the line, where f1(x)=λ1x, f2(x)=λ2x+1-λ22,f3(x)=1-λ1+λ1x, x∈[0,1]. In this paper, we proved that if 1-2λ1-λ22⩾λ, where λ≡max{λ1,λ2}, then the exact Hausdorff centered measure Cs of K(λ1,λ2) equals 1, where s is the Hausdorff dimension of K(λ1,λ2).

Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077905000792
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:26:y:2005:i:2:p:313-323

DOI: 10.1016/j.chaos.2005.01.008

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().