The circle as an attractor of an iterated function system on the plane

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Abstract

We give an iterated function system (IFS) on the plane with the circle as attractor. In doing this, we also give a sufficient condition for radially contracting functions on the plane (or on Rn) to be a contraction. A counterexample shows that radial contractiveness is not enough to be a contraction. © 2006 Elsevier Inc. All rights reserved.

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Demir, B., Dzhafarov, V., Koçak, Ş., & Üreyen, M. (2007). The circle as an attractor of an iterated function system on the plane. Journal of Mathematical Analysis and Applications, 332(1), 735–740. https://doi.org/10.1016/j.jmaa.2006.10.067

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