On the magnification of Cantor sets and their limit models
type: Item
instance of: scholarly article
title: On the magnification of Cantor sets and their limit models
zbMATH Open document ID: 0843.28002
DOI: 10.1007/BF01299636
author: Tim Bedford
author: Albert M. Fisher
published in: Monatshefte für Mathematik
publication date: 1996-08-11T00:00:00Z
full work available at URL: https://eudml.org/doc/178710
review text: The authors show that cookie-cutter sets \(C\) have well defined limit models for their infinitesimal geometry. It turns out that diffeomorphic copies of \(C\) have the same limit models. To prove this they introduce magnifications around translations of points as topological flows on the hyperspace of closed non-empty sets in the line equipped with the Fell topology. They also point out the relation with Sullivan's scaling function and to the definition of fractal sets as given by Wicks.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 854276
zbMATH Keywords: cookie-cutter Cantor set
zbMATH Keywords: scenery
zbMATH Keywords: scaling function
zbMATH Keywords: fractal sets
reviewed by: Hermann Haase
MaRDI profile type: Publication
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OpenAlex ID: W2005898561
description: scientific article; zbMATH DE number 854276