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2016 A Non Self-Similar Set
Emma D’Aniello, T. H. Steele
Real Anal. Exchange 41(2): 347-350 (2016).

Abstract

For each $s \in (0,1]$, we give an example of a nowhere dense perfect set $E$ contained in the unit interval with $\dim_{\cal H} (E) = s$, which is not an attractor for any iterated function system composed of weak contractions. This answers a problem posed by Zoltán Buczolich at the Summer Symposium in Real Analysis XXXIX (June 8-13, 2015, St.~Olaf College, Northfield, MN).

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Emma D’Aniello. T. H. Steele. "A Non Self-Similar Set." Real Anal. Exchange 41 (2) 347 - 350, 2016.

Information

Published: 2016
First available in Project Euclid: 30 March 2017

zbMATH: 06848934
MathSciNet: MR3634899

Subjects:
Primary: 26A18 , 28A78
Secondary: 28A80

Keywords: attractor , Cantor set , iterated function system , self-similar set

Rights: Copyright © 2016 Michigan State University Press

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