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Strongly-Fibred Iterated Function Systems and the Barnsley–Vince triangle

Volume 125 / 2023

Krzysztof Leśniak, Nina Snigireva, Filip Strobin Banach Center Publications 125 (2023), 81-90 MSC: Primary 28A80; Secondary 47H09, 37A30. DOI: 10.4064/bc125-7


We review the theory of semiattractors associated with non-contractive Iterated Function Systems (IFSs) and demonstrate its applications on a concrete example. In particular, we present criteria for the existence of semiattractors due to Lasota and Myjak. We also discuss the Kieninger criterion which allows us to characterise when a semiattractor is strongly-fibred. Finally, we consider a specific example of a non-contractive IFS introduced by Barnsley and Vince. We find an invariant measure for this system which allows us to describe its semiattractor. The difficulty in analysing this IFS stems from the fact that it is neither eventually contractive nor contractive on average.


  • Krzysztof LeśniakFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University in Toruń
    Chopina 12/18, 87-100 Toruń, Poland
  • Nina SnigirevaAtlantic Technological University
    ATU Sligo, Ash Lane, Sligo, F91 YW50, Ireland
  • Filip StrobinInstitute of Mathematics, Lodz University of Technology
    al. Politechniki 8, 93-590 Łódź, Poland

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