2022/04/01 by Elismar R. Oliveira, Oliveira, Elismar R.
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2204.00373
openalex publication_date 2022/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of generalized iterated function systems (GIFS) was introduced by Mihail and Miculescu in 2008. We provide a new approach to study those systems as the limit of the Hutchinson-Barnsley setting for infinite iterated function systems (IIFS) which has been developed by many authors in the last years. We show that any attractor of a contractive generalized iterated function system is the limit with respect to Hausdorff-Pompeiu metric of attractors of contractive infinite iterated function systems. We also prove that any Hutchinson measure for a contractive generalized iterated function system with probabilities is the limit with respect to the Monge-Kantorovich metric of the Hutchinson measures for contractive infinite iterated function systems with probabilities.