Counterexamples for IFS-attractors
Dynamical Systems
2016-06-29 v1
Abstract
In this paper, we deal with the part of Fractal Theory related to finite families of (weak) contractions, called iterated function systems (IFS, herein). An attractor is a compact set which remains invariant for such a family. Thus, we consider spaces homeomorphic to attractors of either IFS or weak IFS, as well, which we will refer to as Banach and topological fractals, respectively. We present a collection of counterexamples in order to show that all the presented definitions are essential, though they are not equivalent in general.
Keywords
Cite
@article{arxiv.1510.03391,
title = {Counterexamples for IFS-attractors},
author = {Magdalena Nowak and Manuel Fernandez-Martinez},
journal= {arXiv preprint arXiv:1510.03391},
year = {2016}
}