Topological measures, image transformations and self-similar sets

This paper introduces a novel idea: the concept of an image transformation. We also introduce the closely related concept of a quasi-homomorphism, and study the properties of these mathematical objects, and give several examples. In particular we investigate iterated systems of image transformations...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2005-09, Vol.109 (1-2), p.65-97
Main Authors: Aarnes, Johan F., Johansen, Ørjan, Rustad, Alf B.
Format: Article
Language:English
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Summary:This paper introduces a novel idea: the concept of an image transformation. We also introduce the closely related concept of a quasi-homomorphism, and study the properties of these mathematical objects, and give several examples. In particular we investigate iterated systems of image transformations, which we believe give a more realistic approach to the study of so called self-similar structures in nature than what is obtained by iterated function systems.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-005-0235-6