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A class of continua that are not attractors of any IFS. (English) Zbl 1259.28013

Summary: This paper presents a sufficient condition for a continuum in \(\mathbb R^{n }\) to be embeddable in \(\mathbb R^{n }\) in such a way that its image is not an attractor of any iterated function system. An example of a continuum in \(\mathbb R^{2}\) that is not an attractor of any weak iterated function system is also given.

MSC:

28A80 Fractals
54F15 Continua and generalizations
37B25 Stability of topological dynamical systems
54H20 Topological dynamics (MSC2010)
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References:

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