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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Attractors of iterated function systems


Authors: P. F. Duvall and L. S. Husch
Journal: Proc. Amer. Math. Soc. 116 (1992), 279-284
MSC: Primary 54H15; Secondary 54E40, 54H20
MathSciNet review: 1132850
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Abstract: In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric $ X$, there is a Cantor set $ C$ such that the disjoint union of $ C$ and $ X$ is an attractor. In the process, it is proved that every such $ X$ is the Lipschitz image of a Cantor set.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1132850-6
PII: S 0002-9939(1992)1132850-6
Keywords: Iterated function systems, attractors, fractal geometry, contractions, Lipschitz mappings
Article copyright: © Copyright 1992 American Mathematical Society