Strongly-Fibred Iterated Function Systems and the Barnsley–Vince triangle
Volume 125 / 2023
Banach Center Publications 125 (2023), 81-90
MSC: Primary 28A80; Secondary 47H09, 37A30.
DOI: 10.4064/bc125-7
Abstract
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.
