Attractors of iterated function systems

Duvall, P. F.; Husch, L. S.

doi:10.1090/S0002-9939-1992-1132850-6

Attractors of iterated function systems
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by P. F. Duvall and L. S. Husch

Proc. Amer. Math. Soc. 116 (1992), 279-284

DOI: https://doi.org/10.1090/S0002-9939-1992-1132850-6

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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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