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Attractors of generalized IFSs that are not attractors of IFSs.
- Source :
-
Journal of Mathematical Analysis & Applications . Feb2015, Vol. 422 Issue 1, p99-108. 10p. - Publication Year :
- 2015
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 422
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 98602159
- Full Text :
- https://doi.org/10.1016/j.jmaa.2014.08.029