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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Attractors of iterated function systems
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by P. F. Duvall and L. S. Husch PDF
Proc. Amer. Math. Soc. 116 (1992), 279-284 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 279-284
  • MSC: Primary 54H15; Secondary 54E40, 54H20
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1132850-6
  • MathSciNet review: 1132850