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Topological version of generalized (infinite) iterated function systems

Author

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  • Dumitru, Dan
  • Ioana, Loredana
  • Sfetcu, Răzvan-Cornel
  • Strobin, Filip

Abstract

Our paper is an attempt to unify various generalizations of IFSs which appeared in the literature in the last years. We extend the notion of a generalized iterated function system (introduced by Miculescu and Mihail in 2008) to the topological and (possible) infinite case. Then we prove that many classical results (for example the existence of a unique attractor) hold for this extended case.

Suggested Citation

  • Dumitru, Dan & Ioana, Loredana & Sfetcu, Răzvan-Cornel & Strobin, Filip, 2015. "Topological version of generalized (infinite) iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 78-90.
    • Handle: RePEc:eee:chsofr:v:71:y:2015:i:c:p:78-90
    DOI: 10.1016/j.chaos.2014.12.005
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    Cited by:

    1. Oliveira, Elismar R., 2017. "The Ergodic Theorem for a new kind of attractor of a GIFS," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 63-71.
    2. Miculescu, Radu & Mihail, Alexandru & Urziceanu, Silviu-Aurelian, 2020. "Contractive affine generalized iterated function systems which are topologically contracting," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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