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Counterexamples for IFS-attractors

Author

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  • Nowak, Magdalena
  • Fernández-Martínez, M.

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.

Suggested Citation

  • Nowak, Magdalena & Fernández-Martínez, M., 2016. "Counterexamples for IFS-attractors," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 316-321.
    • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:316-321
    DOI: 10.1016/j.chaos.2015.12.006
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    Cited by:

    1. Klinga, Paweł & Kwela, Adam, 2022. "Comparison of the sets of attractors for systems of contractions and weak contractions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Klinga, Paweł & Kwela, Adam & Staniszewski, Marcin, 2019. "Size of the set of attractors for iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 104-107.

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