2018/08/29 by Díaz, Lorenzo J., Matias, Edgar
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1808.10283
We consider iterated functions systems (IFS) on compact metric spaces and introduce the concept of target sets. Such sets have very rich dynamical properties and play a similar role as semifractals introduced by Lasota and Myjak do for regular IFSs. We study sufficient conditions which guarantee that the closure of the target set is a local attractor for the IFS. As a corollary, we establish necessary and sufficient conditions for the IFS having a global attractor. We give an example of a non-regular IFS whose target set is nonempty, showing that our approach gives rise to a "new class" of semifractals. Finally, we show that random orbits generated by IFSs draws target sets that are "stable".