Attractors of generalized IFSs that are not attractors of IFSs

作者：Strobin Filip^*

来源：Journal of Mathematical Analysis and Applications, 2015, 422(1): 99-108.

DOI：10.1016/j.jmaa.2014.08.029

• IFSs
• Generalized IFSs
• Attractors
• Cantor sets

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.

• 出版日期2015-2-1