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Session 9. General forms of self-similarity in algebra and topology
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Iterated function systems and their attractors |
Magdalena Nowak, Institute of Mathematics, Jan Kochanowski University in Kielce, Poland
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We deal with the part of Fractal Theory related to iterated function systems on a topological space X. By an Iterated Function System (IFS) we understand a dynamical system generated by a finite family of continuous self-maps of X. An \emph{attractor} is a compact set, invariant for such a family. In other words, an IFS-attractor is the unique fixed-point of the dynamical system acting on the hyperspace of non-empty compact sets endowed with the Vietoris topology.
We consider topological and contracting properties of iterated function systems. We present the topological definition of IFS-attractor and show the metrization theorem connected with this subject.
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