Attractors of generalized IFSs that are not attractors of IFSs |
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Authors: | Filip Strobin |
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Institution: | 1. Institute of Mathematics, ?ód? University of Technology, Wólczańska 215, 93-005 ?ód?, Poland;2. Institute of Mathematics, Jan Kochanowski University in Kielce, ul. ?wietokrzyska 15, 25-406 Kielce, Poland |
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Abstract: | Mihail and Miculescu introduced the notion of a generalized iterated function system (GIFS in short), and proved that every GIFS generates an attractor. (In our previous paper we gave this notion a more general setting.) In this paper we show that for any m≥2, there exists a Cantor subset of the plane which is an attractor of some GIFS of order m , but is not an attractor of a GIFS of order m−1. In particular, this result shows that there is a subset of the plane which is an attractor of some GIFS, but is not an attractor of an IFS. We also give an example of a Cantor set which is not an attractor of a GIFS. |
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Keywords: | IFSs Generalized IFSs Attractors Cantor sets |
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